{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f8ba3161",
   "metadata": {},
   "source": [
    "# Interp 7: Building in structural biases"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6535c1f2",
   "metadata": {},
   "source": [
    "In the previous notebook, we have shown how to test hypothesis for a trained model. If you are content with the insights (tree structure and symmetry properties), you can simply stop here. However, if you want to leverage these properties and apply these inductive biases to your neural network, this notebook walks you through a few possiblities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3b818211",
   "metadata": {},
   "outputs": [],
   "source": [
    "from kan import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e9926ed",
   "metadata": {},
   "source": [
    "Case 1: Separability\n",
    "\n",
    "* if you have confirmed that $f(x_1,x_2,x_3,x_4)=f_1(x_1)f_2(x_2)f_3(x_3)f_4(x_4)$, you can make the last operation to be multiplication. And you can use model.module to create modules so that variables do not interact."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cbe4788b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x200 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[4,[0,1]], mult_arity=4, grid=5, k=3) # note [0,1] means in the output layer, 0 sum node and 1 mult node\n",
    "x = torch.rand(100,4)*2-1\n",
    "model(x)\n",
    "model.plot(beta=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f5aff4ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JRPEzHseBtiovL2epqaksMjKSDR8+nDVp0kTxYa9JkyZs2LBhLDIykp06dYqVl5erpM03/fXXu+KSn5/PfHx8WIMGDdgPP/zAysvLWXFxMQsNDWUfffQRW7hwIZNKpezJkyds6dKlzM7Ojq1Zs6ZGJ7KysjJ28uRJtmLFCjZ06FDWuHFjxRu1adOmbMSIEWzVqlUsPT2dPX36VI3PVjvVNAe2trasffv2DAAbPnw4y8nJ4f0UdM7+/ftZ/fr1mb29PduzZw97/Pix2o8DXXfv3j32448/slmzZrHu3bszU1NTBoAZGxszd3d3FhYWxvbu3cvu3LlT49dFE+chbadXxUUul7O5c+cya2trJhaLFYnKy8tjTk5ODADz8vJiFRUVjDHGpFIpW7VqFXNwcGBpaWkvfMxbt26x3bt3s9DQUNalSxdmZGTEADAzMzPWo0cPNnv2bHbo0CH24MEDjT1XbVXbHBgZGbHFixfzDF3n5eTksMDAQAaAtWrVSqXHwZvg6dOnLCMjg61Zs4Z9+OGHrHnz5ooPjY0aNWJDhgxhy5cvZydOnGClpaUvfBx1nId0kV4Vl2vXrrH69euzmTNnMqlUqvj+i5LK2LNeiEgkYkOGDGFSqZSVlJSwlJQUtnTpUjZo0CDWsGFDxRvM2dmZjRo1iq1bt46dOXNG6XHIM6rIAambtWvXMoFAQDlQgYcPH7LDhw+zOXPmsPfee4+Zm5szAMzQ0JB17tyZTZkyhUVHR7ObN28qiggdA8/w33xDhWJjYyGVSjF+/HgIhUKwl0yEq/qZiYkJJk6ciGHDhqFDhw64evWq4qatLl26YOzYsYqbtnhtfKVL6pKDoKAg3L17V6uXydcFlZWVsLa2phyoQMOGDTFw4EDFjavPb7CWmpqKxMRErFu3DsCzDdY8PDwglUrpGACgN8WFMYbU1FS4uLhAJpMhPDwccrkcAFBeXo6CggIAzzZpCg8PVyyU17BhQ4waNQpWVlZwdHTElClTFMtNaMPGV7qkrjkwMjLCpUuX9OLA4oVyoF6GhoZwc3ODm5sbJk2aBAB49OiRYjmm1NRUnDhxAh07dqTXn1OPSeWkUinr2bMnGzRoEPv555+ZgYGBYjjrZV9t27ZleXl5rF27dmzLli28n4ZOoxzwRzngSyqVsh49etDrz/RoWEwgEMDIyAhPnz6FQCCAsbExZDIZgGef5iorK5V+r0rV71VWVtLSEXVEOeCPcsBX1WtOr78eDYsJhUI4Ozvj+PHjcHV1xYkTJxTjmU+ePMGHH36InJwcdOjQAVFRUYoVVs3MzFBQUIC8vDy0aNGC51PQeZQD/igHfNHr/396U1wAoG/fvvj+++9x+fJl9O7dW7GswuPHjxVLPlhaWqJjx46KTweMMaxfvx7W1tZo27Ytt9j1BeWAP8oBX/T6P6NX27/16dMHLVu2xLJly1BcXPzK32eM4f79+1i7di1GjhypV3tl8EI54I9ywBe9/s/oVXGxsbFBREQEUlJS8MUXX6C0tPSF0wAZY8jLy8OUKVNgbm6OKVOmaDha/WRjY4OFCxciLS2NcsAJ5YCv2rz+kydP1r/XX3NzB9RPLpez0NBQxd3zAQEB7Pfff2dFRUVsw4YNbNmyZSw6OpqVlpaylJQU5uXlxVxcXFhmZibv0PWKVCplK1asYJaWlpQDTigHfNXk9ff09GQGBgbsp59+4h22SunVkvvLly/HnDlzsH79etjZ2WHBggXIzc2Fh4cHOnbsCBsbG0gkEqSnp+P333+Hl5cXVqxYAVdXV96h6x2ZTIYDBw5g2rRpKC8vh5eXF+VAw6pyQMcBH6/7+nft2lWxu+ypU6f0Zg8avSkuO3bswNixY/Hll18iIiICACCRSHDkyBHEx8fjxo0bePr0KWxtbeHm5oahQ4eiZ8+eMDEx4Ru4nuvTpw/u3r2LNm3aUA44+ftxUFBQgHv37mHIkCGYMGEC5UDNXuc8JJFI4Onpifr16yMlJQXW1ta8w64zvSgucXFxGDhwIEJCQhAVFfWPzXfkcjkqKiogk8lgZGTEZbOgN1FJSQns7e2xePFihIWFUQ44qzoOysvL0axZM0ybNg1fffUV77DeGK86D126dAleXl549913kZCQAFNTU06RqobOF5fU1FT07t0bPj4+OHDggGLeOOHv8OHDGDx4MK5du4ZWrVrxDoc8Z+TIkbhy5QrOnTvHOxTynJMnT6Jv377w9/fH3r17dfp8ptOzxS5fvgw/Pz906dIFu3fv1ulE6COxWAxXV1cqLFpIJBLh/PnzyMrK4h0KeY6Xlxf27duHQ4cOITQ09KWLXmo7nS0uWVlZ8Pb2hpOTE44cOaLzXUh9I5fLERsbC5FIxDsUUg0fHx8YGBggNjaWdyjkbwYMGIDNmzdjw4YNWLRoEe9wak0ni8vjx48VB0diYiJsbGx4h0T+JiMjAzk5ORgwYADvUEg1bG1t0bNnT8TExPAOhVQjJCQE33zzDRYsWIDNmzfzDqdWdG75l9LSUohEIuTk5OC3337DW2+9xTskUg2xWAw7Ozt4eHjwDoW8gEgkwty5c1FcXAxLS0ve4ZC/mTdvHrKzszFx4kQ4ODhg8ODBvEOqEZ3quUilUgQGBuLChQuIi4uDi4sL75DIC4jFYvTv35/2xNFiIpEIFRUV+M9//sM7FFINgUCAVatWISAgAB9++CGOHz/OO6Qa0ZniwhjDp59+isTERBw8eBBdu3blHRJ5gdu3b+PixYs0JKblWrZsidatW0MsFvMOhbyAUCjErl274OXlhQEDBuDixYu8Q3ptOlNcPv/8c2zbtg07duyAt7c373DIS4jFYhgZGVGedIBIJEJsbKxizxGifUxMTHDo0CE4OzvD29sbt2/f5h3Sa9GJ4rJmzRosXrwYkZGRGDVqFO9wyCuIxWK89957sLKy4h0KeQWRSIRHjx4hIyODdyjkJaysrBAfHw9zc3N4e3sjNzeXd0ivpPXFZe/evQgLC8Ps2bMxffp03uGQV3jy5AmOHTtGQ2I6wsPDA/b29jQ0pgMcHR2RlJSEwsJC+Pn5vdZy/jxpdXE5evQoRo8ejY8//hhLly7lHQ55DUlJSaisrKT7W3SEgYEB/Pz8aEqyjnB2dkZCQgKuXLmCgIAAxbbJ2khri0tmZiYGDx6MPn364LvvvvvHemFEO4nFYrRr1w7NmjXjHQp5TSKRCJcuXcKtW7d4h0Jeg5ubGw4fPoxff/0VwcHBkMvlvEOqllYWl+vXr8PX1xdt27bFgQMHFFuBEu0mlUoRHx9PvRYd069fPxgZGdHQmA754IMP8P333yM6OhqzZ8/mHU61tK64ZGdnw9vbG/b29oiLi4OFhQXvkMhrSk1NRV5eHl1v0TFWVlZ4//33aWhMxwwfPhxr1qzBt99+ixUrVvAO5x+06g63wsJC+Pj4oKKiAseOHYO9vT3vkEgNiMViNGjQgO5B0kEikQjTp09HYWGhXuwl8qaYMmUKJBIJwsPD0aBBA4wePZp3SApa03MpLy/HoEGDcOfOHSQmJuLtt9/mHRKpIbFYDD8/PwiFWvO2Iq9JJBJBKpUiKSmJdyikhhYuXIhx48YhODgY8fHxvMNR0IqzgEwmw8cff4y0tDTFBWGiW65fv46rV6/SkJiOatq0Kdq3b0/XXXSQQCDAxo0b4e/vj2HDhiE9PZ13SAC0oLgwxjBt2jQcOnQI+/btg5eXF++QSC2IxWKYmJigb9++vEMhtSQSiRAXFwepVMo7FFJDhoaG2LNnDzp27Ag/Pz9cvXqVd0j8i8s333yD9evXY/PmzfSpV4eJxWJ88MEHNAFDh4lEIuTn5+PUqVO8QyG1YGZmhpiYGDRq1Aje3t64f/8+13i4FpctW7bgiy++wDfffIOQkBCeoZA6yM/Px4kTJ+jDgY7r0qULHB0daWhMh9na2iIxMRHAsw3h8vPzucXCrbgcPnwYEyZMwNSpUzFv3jxeYRAVSEhIgEwmg7+/P+9QSB0IhUL4+/vTlGQd17hxYyQlJeHhw4cYMGAAysrKuMTBpbgcP34cI0aMQEBAAFatWkV33+s4sVgMNzc3ODk58Q6F1JFIJMK1a9dw7do13qGQOvjXv/6FuLg4nD17FiNGjOByHU3jxaVqn4/u3btj165dNG1Vx1VWViIhIYGGxPREnz59YGpqSkNjesDd3R0//vgj4uLiMHHiRDDGNNq+Rs/st2/fhre3N1q0aIGffvoJJiYmmmyeqMGJEydQWFhIS77oCQsLC/Tu3ZuGxvSEr68vtm3bhu+++w4LFizQaNsau0M/NzcX3t7eMDc3R0JCAu31oSfEYjHeeustdOzYkXcoREVEIhEmT56Mx48fw87Ojnc4pI5Gjx6NnJwchIeHw9HREVOmTNFIuxrpuRQXF8PPzw8FBQVISkqCo6OjJpolasYYg1gshr+/P1030yP+/v6QyWRISEjgHQpRkVmzZmHmzJkIDQ3F/v37NdKm2otLZWUlAgICcOXKFSQmJsLZ2VndTRINuXLlCm7cuEHXW/RM48aN0alTJxoa0zPLly/HqFGj8NFHH+Hnn39We3tqLS5yuRzBwcH49ddfcfjwYbi5uamzOaJhYrEYZmZm+OCDD3iHQlRMJBIhMTERFRUVvEMhKiIUCrFt2zb07t0bgwcPxrlz59TbnjoffM6cOYiOjsb3339PJyA9JBaL0bdvX5iZmfEOhaiYSCTCkydPcOLECd6hEBUyMjLCgQMH0Lp1a/j6+uLGjRtqa0ttxWXFihVYsWIF1qxZg+HDh6urGcLJo0ePkJqaSkNiesrNzQ2NGzemKcl6yNLSEnFxcbCxsYG3tzckEola2lFLcfn+++8RHh6Ozz//XGMzE4hmxcfHQy6Xw8/Pj3coRA0EAgFEIhFiYmI0fn8EUb/69esjKSkJZWVl8PX1xZMnT1TehoDV4Z2zZMkSXLlyBWFhYWjSpEmN/tbBwaG2zRINWrJkCcaNG1fjv/Pz80NGRoYaIiKqtmTJEly8eLFWq2XQcawbqnLs5+eHPn361Ojm9drmuE73uZiammLWrFlYtGgRBg0ahBEjRtAd93rG1NS0xm8uxhgCAgLUFBFRNVNTU4SEhCA8PBw7d+7kHQ5RA1NTUyxfvhy7du3C3LlzMW/ePLi4uKi1zTpXgvbt2yM6Ohr379/H+PHjcfXqVepGv+Hi4uIQHh7OOwxSA71794apqWm1wyOMMfz222+orKzkEBlRFScnJ8ybNw+fffYZvvnmG2zcuFGt52qVdDOMjIwwa9YszJkzB+vWrcO0adPw22+/UZF5Qw0dOpRuqtRBUVFR6Nat2z++HxkZiczMTNoITg8IBAK0atUK27dvR0lJCZYtW6a2tlQ2hiUQCODi4oK1a9ciNDQU8fHxmDFjBhWYNxDdG6GbBAIBGjdu/I9jNiIiAqGhoejVqxeKioo4RUdUSSgUYubMmcjKysLvv/+unjZU/YACgQAtW7bEokWL0KFDB2zbtk3VTRAtIpPJcOfOHaXvjRo1ilM0pK7i4uLw+eefK/5/8eJFnDx5EgDw5Zdf0jbkekQgEGDdunXw8fFRSydAbVffBQIBgoKCsGzZMuq96LGAgAAMGzZMkeM7d+5gx44dfIMitWZsbIzIyEjF/7t3744OHToAeHZM5+Tk8AqNqIFAIMCvv/6K+fPnq/yx1T61KyMjA5MnT1Z3M4STzMxMJCYmKj7tdu/eHYaGGltsm6jBL7/8gri4OOTn5yMoKEjpZxkZGbh69SqfwIhauLq6Ii0tDaWlpSp9XLWfBWxsbJCSkgLGGF3k1TMSiQTp6emws7PDunXrsGjRIq57dhPV8PDwgLu7OwAgLS1N6WdNmjSBra0t5VnPJCUlwd3dHWfPnlXZY2rkppTU1FRMnDhRE00RNZDL5UhISEBWVpbS9z09PdGoUSMAz05C8+fPx/Hjx3mESFTs2LFj2L9/f7UfCOvVq8chIqJORkZGmDx5Mg4dOqSyx9RIcbGyssKdO3fw6NEjTTRHVOzjjz/GrVu3EBAQALlcrvj+zZs3Ff9u3bo1/P390alTJx4hEhUzMzND06ZNq/1Zeno6zp8/r9mAiNoFBwdj5cqV//gQWVsau51eLBajV69ekEqlmmqSqMjQoUMxadIkJCQkKGaCMcaUZhUBz3oyRP81atQIPXr04B0GUTGBQICjR49ixIgR+O9//1vnx9NYcTE0NMTBgwfh7+9Ps8d0zJAhQwAAdnZ2yM7ORnl5OSIiIrBw4ULOkRFevLy8lHqxRD+YmJggPj4e//73v7F+/fo6navrXFwYY6/95erqirCwMHz11Vd1bZZo0PM5TEpKQv/+/bFr165//OzvX0R31OQ4ZowhJiamVguaEn5eN7dWVlbYvn07pFIpli9fXuv26jRbzNzcvMZjr46OjrCysqpLs0SDqsvxuHHj4Ojo+Mrc086juqE2xzEAxf0vRPvVJsc9e/bEf/7zn1q3Wacl9+vSLabVk3UD5Vj/UY71H48c1+mdIRQKq/1au3YtDAwMsHr16hf+DtENL8rf1q1bYWRkhPz8fMqxjntR/qZPn46mTZtCIBBQjnVcdbl79OgRXFxc8K9//Qt5eXkqz7Fa3h3Tpk3D3LlzMWPGDERHR6ujCcKZv78/5HI54uPjeYdC1IAxBrFYDH9/f7r5WQ8VFRWhf//+KC0tRXJyslo2fVPbR4/Fixdj7NixCAoKQnJysrqaIZw0atQIXbp0oT3W9dTly5dx69YtDBgwgHcoRMWePn2KwYMH488//0RiYiKaNWumlnbUunDl5s2b4ePjgyFDhuD06dPqaopwIhKJkJiYSEvs66GYmBhYWFjg/fff5x0KUSG5XI4xY8bg5MmTiImJQfv27dXWlloHTQ0NDbFv3z60b98e/fv3x7Vr19TZHNEwkUiEoqIipKSk8A6FqJhYLEbfvn1hamrKOxSiIowxhIWF4cCBA9i9ezfee+89tban9ity5ubmEIvFcHBwQL9+/fDgwQN1N0k0pEOHDmjSpAkNjemZnJwcpKWlQSQS8Q6FqNDSpUuxdu1arF+/XnFjtDppZLqHvb09kpKSIJPJ4Ovri4KCAk00S9RMIBBAJBIhJiaGbprUI3FxcQAAPz8/zpEQVdm6dSs+++wzREREYMKECRppU2NzCZs0aYLExERkZWVh4MCBKC8v11TTRI1EIhHu3LmjkrWIiHYQi8Vwd3eHo6Mj71CICsTExOCTTz7BhAkTsGDBAo21q9GJ6m3btkVsbCxOnz6NkSNHQiaTabJ5oga9evWChYUFDY3pifLyciQnJ9OQmJ747bffEBgYiEGDBmHdunUanVau8bugPD09sW/fPsTExGDy5Mk0nKLjTE1N4e3tTcVFTxw7dgwlJSU0BVkPXLp0Cf7+/nB3d0d0dDQMDAw02j6XW2xFIhG2bNmCTZs20cq6ekAkEiE9PR0SiYR3KKSOYmJi0KxZM7Rt25Z3KKQOsrKy4OPjg6ZNm+LIkSNcZv1xW79h7NixWLJkCSIiIhAVFcUrDKIC/fv3B/D/C8FENzHGEBsbC5FIRHfl67C8vDx4e3vD0NAQCQkJsLa25hIH18WB5syZg2nTpmHSpEk4ePAgz1BIHTRo0AAeHh40NKbjLly4gKysLBoS02ElJSXw9/dHbm4ukpOTFduQ88C1uAgEAkRGRmLEiBEYOXIkjh07xjMcUgcikQjJyck0C1CHxcTEwMrKCj179uQdCqmFyspKBAYG4uLFi4iPj0erVq24xsN9WVOhUIgdO3agZ8+eGDhwIC5cuMA7JFILIpEIpaWl+OWXX3iHQmpJLBbD29sbxsbGvEMhNcQYw/jx45GUlIRDhw6hc+fOvEPiX1wAwNjYGIcOHUKrVq3g4+ODW7du8Q6J1FCbNm3QvHlzGhrTUQ8ePMCZM2doCrKOmjdvHnbu3ImdO3eiX79+vMMBoCXFBQDq1auH+Ph4WFpaol+/fsjJyeEdEqkBgUCAAQMGQCwW0/RyHRQbGwuhUKiYnEF0x8qVK7Fs2TKsXLkSI0eO5B2OgtYUF+DZheGkpCQUFRXBz88PRUVFvEMiNSASiXD//n2cO3eOdyikhsRiMbp37w57e3veoZAaiI6OxowZMzBnzhyEhYXxDkeJVhUXAGjRogUSExPxxx9/YOjQobScuw7p0aMHrKysaGhMx5SWluLo0aM0JKZjkpOTERQUhDFjxmDJkiW8w/kHrSsuAPDuu+/iyJEjSElJQVBQUJ32fyaaY2xsDF9fXyouOubnn39GeXk5TUHWIadPn8aQIUPg7e2NLVu2aOV9SVpZXADg/fffR3R0NPbu3YuZM2fSOL6OEIlEyMzMxP3793mHQl5TTEwMWrVqBVdXV96hkNdw7do19O/fH++88w72798PIyMj3iFVS2uLCwAEBARg/fr1WLVqFf7973/zDoe8Bl9fXxgYGCA2NpZ3KOQ1yOVyxV35RPs9fPgQ3t7ecHBwQGxsLMzNzXmH9EJaXVwAYOLEiViwYAHmzJmDHTt28A6HvIKdnR28vLxoaExHZGZmIjs7m4bEdEBhYSF8fHwglUqRlJSk9ZMvDHkH8DoiIiKQnZ2NcePGwcHBgTYx0nIikQjz589HSUkJLCwseIdDXiImJga2trbo3r0771DIS5SXl2PgwIHIysrCiRMn0KRJE94hvZLW91yAZ/dQbNiwAQMGDMCwYcOQmprKOyTyEiKRCE+fPsXRo0d5h0JeQSwWw9fXF4aGOvE5840kk8kwatQoZGRkIDY2VmdWrNaJ4gIABgYG2L17Nzp37gw/Pz9cvnyZd0jkBVxcXODq6kpDY1ru7t27uHDhAg2JaTHGGCZPnowjR45g37598PT05B3Sa9OZ4gI825gqJiYGTk5O8Pb2RlZWFu+QyAuIRCLExsbSNHItJhaLYWhoCB8fH96hkBdYuHAhNm3ahM2bN+vcpAudKi4AYGNjg8TERBgYGMDHxwePHz/mHRKphkgkgkQiwenTp3mHQl5ALBajZ8+e3Pb7IC8XFRWFiIgILF68GMHBwbzDqTGdKy4A8NZbbyEpKQkSiUSxGi/RLp6enrC1taWhMS1VVFSEX3/9Vec+Db8pDh48iEmTJiE0NBRz587lHU6t6GRxAQBXV1fEx8fj/PnzCAwMhFQq5R0SeY6hoSH8/PwQExPDOxRSjeTkZFRUVFBx0ULHjh3DyJEjMXz4cKxcuVIr775/HTpbXACga9euOHjwIBITE/HJJ5/QXfxaRiQS4eLFi7hz5w7vUMjfiMVitGnTBs7OzrxDIc+5cOECBg4ciJ49e2Lnzp0QCnX3FK27kf/Fx8cH27dvx/bt2zF//nze4ZDnVO3jTUNj2kUmkyEuLo56LVrm1q1b8PHxQatWrXDo0CGYmJjwDqlO9GJy+0cffYScnBzMnDkTDRs2RGhoqOJnjDHk5eWhuLgYlpaWsLe319lupq6xtrZGr169IBaLMWLECMoBR88fB5cvX0Zubi5NQdawl52LHj16BG9vb1haWiI+Ph716tXjHK0KMD0SHh7OBAIB27NnD8vPz2erVq1izs7ODIDiy9nZma1atYrl5+fzDlfv5efns8GDByu9/pQDzXrRcSAUCllkZCTlQANedS7KyspinTt3Zo6OjuzGjRu8w1UZvSouMpmMjR49mhkaGjJTU1MmEAiYQCBQSmjV9ywsLFhiYiLvkPVWYmIis7Cw+EdhoRxoTlUOqjsOqvJAOVCvl+Wg6v8GBgbM3NycnTt3jne4KqXz11yeJxQKMXz4cEilUpSXl4M9K55Kv1P1vbKyMvj5+SEpKYlTtPorKSkJfn5+KCsrq/bnlAP1ez4H1R0HACgHavaqHFT9XyaToby8HBKJhEeYaiNg1b3rdFRBQQGcnJxQWlr6WjPHhEIhzMzMcO/ePdjY2Kg/wDdAVQ7Kyspe6+58yoHqUQ74oxzowWyx5+3cufO1CwvwbC+L0tJS7Nq1S82RvTmqcvC6y75QDlSPcsAf5UCPei6MMbRq1Qo3b96s0f0uAoEALVq0wPXr12kGUx1RDvijHPBHOXhGb4pLbm4uHBwc6vT32r75jrajHPBHOeCPcvCM3gyLFRcX1+nvi4qKVBTJm4tywB/lgD/KwTN6U1wsLS3r9Pd6cdMSZ5QD/igH/FEOntGb4mJvbw9nZ+caj1UKBAI4OzvDzs5OTZG9OSgH/FEO+KMcPKM3xUUgEGDq1Km1+tvQ0FC9uIDGG+WAP8oBf5SDZ/Tmgj5Ac8u1AeWAP8oBf5QDPeq5AM92qTx48CAEAsErl6oWCoUQCAQ4dOiQ3iRTG1AO+KMc8Ec5gH4tXFnlVev5VK2plJSUxDtUvUU54I9ywN+bnAO9LC6MPVuJdPXq1dWuRLp69WpWUFDAO0S9Rzngj3LA35uaA7265lIdxhgeP36MoqIi1KtXD3Z2dnpzwUxXUA74oxzw96blQO+LCyGEEM3Tqwv6hBBCtAMVF0IIISpHxYUQQojKUXEhhBCiclRcCCGEqBwVF0IIISpHxYUQQojKUXEhhBCiclRcCCGEqBwVF0IIISpHxYUQQojKUXEhhBCiclRcCCGEqNz/AOUZdz5ieJ0zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 500x200 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to specify a module, you need to specify the start layer (0 in this case),\n",
    "# you also need to specify which neurons belong to this module\n",
    "# the rule might be a bit complicated to explain, but you will observe the pattern with a few examples. \n",
    "model = KAN(width=[4,[0,1]], mult_arity=4, grid=5, k=3) # note [0,1] means in the output layer, 0 sum node and 1 mult node\n",
    "x = torch.rand(100,4)*2-1\n",
    "model(x)\n",
    "\n",
    "model.module(0,'[0]->[0]')\n",
    "model.module(0,'[1]->[1]')\n",
    "model.module(0,'[2]->[2]')\n",
    "model.module(0,'[3]->[3]')\n",
    "\n",
    "model.plot(beta=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4d5137cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x200 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[4,[0,1]], mult_arity=4, grid=5, k=3) # note [0,1] means in the output layer, 0 sum node and 1 mult node\n",
    "x = torch.rand(100,4)*2-1\n",
    "model(x)\n",
    "\n",
    "model.module(0,'[0,1]->[0,1]')\n",
    "model.module(0,'[2,3]->[2,3]')\n",
    "\n",
    "model.plot(beta=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "34a7bce5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x200 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[4,[0,1]], mult_arity=4, grid=5, k=3) # note [0,1] means in the output layer, 0 sum node and 1 mult node\n",
    "x = torch.rand(100,4)*2-1\n",
    "model(x)\n",
    "\n",
    "model.module(0,'[0,1]->[2,3]')\n",
    "model.module(0,'[2,3]->[0,1]')\n",
    "\n",
    "model.plot(beta=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "816a4250",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x200 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[4,[0,1]], mult_arity=4, grid=5, k=3) # note [0,1] means in the output layer, 0 sum node and 1 mult node\n",
    "x = torch.rand(100,4)*2-1\n",
    "model(x)\n",
    "\n",
    "model.module(0,'[0]->[0]')\n",
    "model.module(0,'[1,2,3]->[1,2,3]')\n",
    "\n",
    "model.plot(beta=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1728aea1",
   "metadata": {},
   "source": [
    "Case 2: you can use model.module smartly to create tree graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "37e983f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 70 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a tree case\n",
    "model = KAN(width=[4,6,2,6,1], mult_arity=4, grid=5, k=3) # note [0,1] means in the output layer, 0 sum node and 1 mult node\n",
    "x = torch.rand(100,4)*2-1\n",
    "model(x)\n",
    "model.plot(beta=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b6c70991",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZeeDiwr7o3SNbFxcXgx7Z3rhxA127doVarUauXLlkOTL/lHfPLL5082JmGerMKIWhz+wMfWbKsjYuLuwjxh6Tl/uawtfIfU3kcwx1TedD716Typ8/v2zXpN5lyGtqLGvi4sKEzSaSazZUety/fx92dnbo3bu3QdtJcfPmTVhZWck2G+1L3p1NV7BgQVlm033Ku7MBvby8ZJsNyLIWLi5mKjY2Flu3bkWvXr3g4eEBIoKLi4tR7oOQ4z6OjJAkCY0aNUKuXLnSfPe/HGbPni3LfTRpJfd9QF+Sch/T1KlTZbuPiWUNXFzMiOg7uN+9Az1btmzpvgM9szJ7B31GybUCQHq9u4JB0aJFM7yCQXo8efIEy5YtQ6tWrd5bgWH48OHpXoGBmTYuLllYytpTU6ZMSV17Sq1Wo3bt2pg1axZu3LhhlBzvrp3l7u6e5rWz5JSy9te3335r1HZTpKxdNnLkSKO3ffr0aTRv3jxTa69lxOvXr7F9+/ZMrx3HTBMXlywmPj4eu3btem/VXHt7+9RVc7/0UCu5PXr0CP369UvXqr+GIEkSmjdvDk9Pz9THDYuQsuryyZMnhbR/8uTJ91aN3rRpk9FumJRj1WtmWri4ZAFKe97H48ePU59X4uLi8tXnlRjamjVr0vW8FUPJ6PNi5Hb8+PEMPe9GTvfv3099Xk/KjMS0Pq+HmQYuLiZIqU8q/NSTFkUvkPj48eM0PynSGNL7pEtDysiTOg3h5cuXHz1p1MPD46tPGmXKxsXFRLz7jPWCBQuCiGBtbZ36jPWwsDBh2cLCwjB06ND3nhGvhPH0d59xr6SHaP3000/QaDQ4c+aM6CgAgCNHjqBevXogIpQrVw7btm0TdoNkcnIyjh49ilGjRqFo0aIgIlhaWqJFixZYvHgxQkNDheRi6cfFRcGeP3+ODRs2oEuXLnBycgIRIUeOHPDz80NQUJBRZx59SkREBEaMGAFra2s4ODhg8uTJ6XoSo6H99ddfICJs3rxZdJT3JCYmoly5cihZsqSibj48ePAgateuDSJCxYoVERQUJPwu/Js3b2L27NmoU6cONBoNiAgVKlTAlClTcP78eeH52OdxcVGYO3fuYO7cuahfvz60Wi2ICGXLlsUPP/yAM2fOKGIsOjIyEqNGjYKNjQ3s7e0xceJEoRfKPyU8PBwuLi7o2LGj6CifdOHCBWi1WkycOFF0lPdIkoT9+/ejZs2aICJUrlwZwcHBivgSf/bsGf7880907NgRDg4OICLkypUL/fr1w65duxRVqBkXF+GSk5Nx/PhxjB07FiVKlAARwcLCAk2bNsWCBQvw4MED0RFTPX36FGPGjIGtrS3s7OwwYcIERQ03vcvb2xvu7u6IjIwUHeWzJk2aBK1Wi//++090lI9IkoS9e/eievXqICJUrVoVu3fvVkSRAd6uErB3714MHjwYefPmBRHB1tYW7du3x6pVqxT9/24uuLgI8OrVK2zevBk9e/aEu7t76lMCe/TogcDAQFmXaZfDs2fPMH78eNjZ2cHW1hZjx45V9BIfmzZtAhFh48aNoqN8UUJCAkqXLo2yZcvKuuCknCRJwu7du1GlShUQEapXr469e/cqpsgAbzNeunQJ06ZNQ9WqVaFSqaBSqVC9enX88ssvuHLliqLymgsuLkby6NEjLFq0CM2aNYOlpWXqDW2jR4/Gv//+a/A7pzMiOjoa33//Pezt7WFjY4PRo0cr/ogwMjIS7u7uaN++vUl8oZw7dw4ajQY//vij6ChfJEkSgoODUalSJRARatasiQMHDoiO9Unh4eFYsWIF2rRpAxsbm9Qnlw4dOhQHDhxQbCHPari4GIgkSTh37hwmTZqE8uXLg4ig0WhQt25dzJkzB7du3RId8bOeP3+OSZMmwcHBAdbW1hg5ciQiIiJEx0qTTp06wcXFBeHh4aKjpNn48eOh0+kQEhIiOspXSZKEoKAgVKhQAUSEOnXq4NChQ6JjfVZcXByCgoLQp08feHp6gojg5OSEzp07Y/369YqagJLVcHGR0Zs3b7Bz50707dsXOXPmBBHB0dERnTp1wl9//aW4i94fevHiBaZMmQJHR0dYWVlh2LBhQqc4p9fmzZtBRPjzzz9FR0mX+Ph4FC9eHBUqVDCZtbckScK2bdtQrlw5EBHq1auHI0eOiI71RZIk4ezZs/jhhx9Sc2u1WtSrVw+//fYbbt++LTpilsLFJZMiIiKwcuVKtG3bFra2tqnPeR8yZAj2799vEqfgL1++xNSpU+Hs7AxLS0sMGTLE5J46GBUVBQ8PD7Rq1cokhsM+dOrUKajVavz888+io6SLJEnYsmVL6pIuDRo0MNrqz5n18OFDLFy4EE2bNoWFhQWICMWLF8eYMWNw7NgxRQ5VmxIuLukkSRIuX76Mn3/+GdWqVUu9eFitWjVMnz4dly9fNpkvt5iYGPz8889wcXGBhYUFBg0ahMePH4uOlSHffPMNnJycTDY/AIwaNQoWFha4cuWK6CjpptfrERgYmPo8oMaNG+PEiROiY6VZTEwMAgMD8e2338LNzQ1EBHd3d3z77bcIDAwUunyRqeLikgaJiYnYv38/hgwZgnz58oGIYGNjg3bt2mHlypUmcz0ixatXr/DLL7/A1dUVFhYW6N+/Px49eiQ6Vobt2LEDRITVq1eLjpIpcXFxKFKkCKpUqWKyR816vR6bNm1KnVbftGlTnDp1SnSsdElOTsaxY8cwZswYFC9ePPX2gGbNmmHhwoUm/VkxJi4unxEdHY2//voLnTp1gqOjI4gIOXPmRN++fREcHCx04cGMio2NxcyZM+Hm5gadToe+ffvi4cOHomNlyvPnz+Hp6YlmzZqZzBnjlxw7dgwqlQozZ84UHSVT9Ho9/v77bxQrVgxEhObNmytmuZv0un37Nn777TfUq1cvdZWAcuXKYdKkSTh79myWeN8ZAheXd9y6dQtz5sxB3bp1U99E5cuXx+TJk3Hu3DmTfRO9fv0as2fPRrZs2aDVatG7d2+DPbrY2Hr27AkHB4csdTQ5bNgwWFlZGe15O4aUnJyMv/76C0WKFAERoVWrVjh37pzoWBkWHR2N9evXf3TQ2adPH+zcudMkDzoNxayLS3JyMv7991+MHj069QjL0tISzZs3x6JFi0z+CysuLg6//fYbPDw8oNFo0KtXryz13Ixdu3aBiLBs2TLRUWT1+vVrFCxYEDVq1DDZ4bEPJScnY926dShUqBCICG3atFHkygTpkZiYiAMHDmDo0KHInz9/6nB527ZtsWLFCpOaDm8IZldcYmJiEBAQgB49erx34a5nz57YvHlzlrhw9+bNG8ybNw85cuSARqNBz549cefOHdGxZPXy5UvkypULjRo1Mtkzyi85fPgwiAhz584VHUVWSUlJWLNmDQoUKAAiQrt27XDx4kXRsTJNkiRcuXIF06dPR/Xq1VMn+lStWhU///wzLl26lCXfp19iFsXl4cOHWLBgAZo0aZI65bBEiRIYO3Ysjh8/nmWODuPj4/HHH38gZ86cUKvV6N69u6Jv1swMPz8/2NnZZZnhvU8ZOHAgrK2ts+T9F0lJSVi5cmXqBBkfHx9cunRJdCzZREREYNWqVWjXrt17tygMHjwY+/btM/oD/ETIksVFr9fjzJkzmDhxIsqWLZt6s1T9+vUxd+7cLHcUHx8fj4ULFyJXrlxQq9X45ptvssR4/efs27cPRISFCxeKjmJQr169Qr58+VCnTh1FrIZtCImJiVi+fDny5s0LlUqFDh06mORU7C958+YNgoOD0a9fv9Sbqx0cHNCxY0f8+eefil38NbOyTHGJi4vDjh074Ofnhxw5cqQu89ClSxds2LAhSy7zkJCQgCVLliB37txQqVTo0qULrl27JjqWQcXExCBPnjyoW7dulv3Cfdf+/ftBRFiwYIHoKAaVkJCApUuXwsvLCyqVCp07d86S72VJknD+/HlMnjw5dQkdjUaDOnXqYPbs2bh586boiLIx6eISFhaG5cuXo3Xr1rC2tk5doG7YsGE4ePCgSdwdnxGJiYlYtmwZ8uTJA5VKhY4dO2a5o73P6d+/P2xsbLLc2eeX9OnTB7a2tllqMsbnJCQkYNGiRaln4V27ds3SZ+GhoaFYvHgxmjdvnrqgbdGiRTFq1CgcPXrUpIfsTaq4SJKEkJAQ/PTTT6lLgKvVatSoUQMzZszA1atXs/RFs8TERKxYsSJ1nNrX1zdLjVN/zcGDB0FE+P3330VHMaqXL18id+7caNCgQZZ+f78rPj4eCxYsSL1+2K1btyx1VP8psbGx2LJlC7777jtky5Yt9VEc3bt3h7+/v+IexfE1JlFcLly4gEGDBiFPnjypDwXy9vbG6tWrFb8EvBz0ej1Wr16dOsOmffv2WWKGTXrExsYif/78qFmzplkMh31o9+7dICIsWbJEdBSjevPmDebPn58687FHjx5mcQan1+tx4sQJjBs3DiVLlkxdJaBx48b4448/TOKMRgUApDAjRowge3t7Sk5OpoSEBBoxYgS5uLh88rUWFhZGTmcciYmJX30NAGrXrh0FBwcbIZFxTZo0iSpVqkSNGzf+6muz6nvg559/pqioKCpdujTlzZuXIiIiyNHRkerXr//Ra7NiH6xevZouXbpEOp2OWrduTRUrVvzsa7Pi/hN9+Xtg+fLlFBYWRs+ePaNu3bpRtWrVjJjs6xRZXBITE0mn0xER0atXr2js2LE0ZMgQKlKkiOBkytK9e3eaN28eOTk5iY4iOwD0999/0927d2ncuHGkVqtFRxIiKSmJbt++TU+ePCF3d3cKDw+nXbt20W+//SY6msGdPXuWKlSoQERE3377La1evZpUKpXgVMpw/vx5unPnDvn4+BAAmjZtGk2cOFF0rPcosrh8CAANHTqUvv/+e3J3dxcdRxEmT55M3bp1owIFCoiOYlC3bt2iX375hWbNmkXOzs6i4yjC4cOHyc3NjUqUKCE6itEAoLZt29K2bdtERxEOADVo0IAOHDggOsoXmURxIXrboY0aNaK9e/ea/dGLv78/OTs7U8OGDUVHMYr4+HgaOnQoDRkyhIoVKyY6jiKUKFGCrly5IjqGUa1du5a6dOlCWq1WdBShpk6dShMmTFD82byy071DpVLR7t27ydvbW3QUoc6fP0/h4eFmU1iIiKysrGjRokX0119/0blz50THUYRz587R4cOHRccwqu7du1ONGjVExxAKAIWGhiq+sBCZ0JlLihMnTpCjoyMVL15cdBSje/ToEc2ePZvmzp0rOooQAGj8+PH03XffUaFChUTHEc7Ly4sePnwoOoZR7dmzh8qUKUMeHh6iowgxfPhwmj17tkmM3ii//H2gWrVq1KNHD9ExjC4qKoomTJhgFhdyP0elUtHPP/9MU6dOpdevX4uOI9yVK1coNDRUdAyjaty4MXXq1In0er3oKEaHt7eOmERhITLB4kJEdPz4cbM6eo+IiKChQ4fSmjVrTOaNZSgqlYrWrFlDrVq1IhM76Zadvb09lSpVSnQMo9uzZw916dLF7A4wunbtSnPmzBEdI81MsrjodDq6evWqWXy5XL16lSZOnEjr1q0z+8KSQqVS0c6dO83yDPZD+/btM7ujeJ1OR6tWraKhQ4fSzZs3RccxiqioKGrcuLFJfQeY3DWXFADIz8+Pli1bJjqKQUiSROvWraPQ0FAaP368Sb2pjOXcuXMUGhpKbdq0ER1FqBo1atCxY8dExzA6ADRp0iRq27YtlS9fXnQcg3jz5g0lJCRQhw4daM+ePaLjpIsi5/Q9e/YsTa+ztbU1cBJxevToQZ06daKWLVtSdHT0F1/r6upqpFTGk5b3QN68eWnJkiVZtrik9XOgtDuz5ZKW/R8yZAiNGTOGli9fboRExjds2DBSq9W0bt26r/aH0r4HFHnm8rUv03d9blkYUxcZGZnm+fxZsQ/4PcB9YO77T2TifWCUFcwy6dy5cyAinDt3TnQUYcy9D8x9/wHuA4D7wJT23yQv6DPGGFM2Li6MMcZkx8WFMcaY7Li4MMYYkx0XF8YYY7Lj4sIYY0x2XFwYY4zJjosLY4wx2XFxYYwxJjsuLowxxmTHxYUxxpjsuLgwxhiTHRcXxhhjsuPiwhhjTHZcXBhjjMmOiwtjjDHZcXFhjDEmOy4ujDHGZMfFhTHGmOy4uDDGGJMdFxfGGGOy4+LCGGNMdlxcGGOMyY6LC2OMMdlxcWGMMSY7Li6MMcZkx8WFMcaY7Li4MMYYkx0XF8YYY7Lj4sIYY0x2XFwYY4zJjosLY4wx2XFxYYwxJjsuLowxxmTHxYUxxpjsuLgwxhiTHRcXxhhjsuPiwhhjTHZcXBhjjMmOiwtjjDHZcXFhjDEmOy4ujDHG5AcFO3fuHL777js4ODiAiODg4IDvvvsO586dEx3NaMy9D8x9/wHuA4D7wBT3X5HFJSkpCX5+fiAiaLVaEFHqn5S/+/n5ISkpSXRUgzH3PjD3/Qe4DwDuA1Pef0UWFz8/P6hUqvc68sM/KpUKfn5+oqMajLn3gbnvP8B9AHAfmPL+K664nDt37osd+eEfJZ8WZpS594G57z/AfQBwH5j6/ivugv6CBQtIq9Wm6bVarZYWLlxo4ETGZ+59YO77T8R9QMR9YOr7rwIA0SHe5erqStHR0Wl+vYuLCz179syAiYzP3PvA3PefiPuAiPvA1PdfccXFwsKCkpKS0vx6nU5HiYmJBkxkfObeB+a+/0TcB0TcB6a+/4obFrO3tzfo602BufeBue8/EfcBEfeBqe+/4opL27Zt0zXO2K5dOwMnMj5z7wNz338i7gMi7gOT33+x8wk+ZuozJORg7n1g7vsPcB8A3Aemvv+KKy6Aac/tlou594G57z/AfQBwH5jy/iuyuJjyXalyMfc+MPf9B7gPAO4DU95/RRaXFOfOnUOvXr3eW0+nV69eijv9MyRz7wNz33+A+wDgPjDF/Vd0cUmRMvao5I40NHPvA3Pff4D7AOA+MKX9V9xsMcYYY6aPiwtjjDHZcXFhjDEmOy4ujDHGZMfFhTHGmOy4uDDGGJMdFxfGGGOy4+LCGGNMdlxcGGOMyY6LC2OMMdlxcWGMMSY7Li6MMcZkx8WFMcaY7Li4MMYYkx0XF8YYY7Lj4sIYY0x2XFwYY4zJjosLY4wx2XFxYYwxJjsuLowxxmSnFR3gS/R6PT18+JCOHDlCRETBwcGUkJBAxYsXJ0dHR8HpjMPc+8Dc95+I+yBl/69cuUKnT58mIqKQkBAqUKCAWew/kWm+B1QAIDrEhwBQSEgIzZw5k/bt20cAyNHRkQBQTEwMeXh4UK9evahnz57k4OAgOq5BmHsfmPv+E3EffLj/REROTk6UlJREMTExlCNHjiy9/0Qm/h6Awuj1emzYsAGenp6oWrUq1q1bh5s3b+Lx48d49OgRQkJC8Msvv6BAgQJo2bIlQkNDRUeWnbn3gbnvP8B9YO77D5h+HyiuuOzcuRNubm7o168foqKiIEkS1q5di2LFiqFs2bK4fPkyJEnCtWvXUKtWLTRv3hwvXrwQHVtW5t4H5r7/APeBue8/YPp9oKjiEhkZiVKlSsHb2xsxMTGQJAkAMHfuXBARrKyscPbsWQCAJEm4efMmihYtipkzZ4qMLStz7wNz33+A+8Dc9x/IGn2gqNliW7dupbCwMJo4cSLZ2dmRSqX67GtVKhUVLFiQhg0bRitWrKBnz54ZManhmHsfmPv+E3EfmPv+E2WNPlBMcdHr9bRz506qXLkyeXl5UXh4OIWFhVFYWBjFxMQQ0duLW1FRUan/HhERQU2bNqX4+Hi6cOGC2B2Qgbn3gbnvPxH3gbnvP1HW6QPFTEWOj4+nO3fuUKtWrWj58uU0e/bs1J/FxcUREVFCQgJ17dqVtNq3sV1cXCgoKIhy5cpFN2/epAYNGgjJLhdz7wNz338i7gNz33+irNMHiikuer2eEhISyM7OjmJjYykiIuKTr3v3lC85OZmIiKytrVM73ZSZex+Y+/4TcR+Y+/4TZZ0+UExxsbS0JGdnZwoNDaVmzZpR3759U3926dIlOnbsGGk0GmrXrh25ubkREZGdnR3pdDqKiooiDw8PUdFlY+59YO77T8R9YO77T5SF+kDkbIIP9evXD+XKlcPLly8hSVLqnw9nSLz7s/Pnz8PT0xMXL14UHV8W5t4H5r7/APeBue8/kDX6QDEX9ImIOnToQHfv3qUdO3YQ0dtZEJ+aJZHy78nJybRs2TIqVaoUFSlSxNhxDcLc+6BDhw50+/Zts91/In4PmPv+E2WNPlBUcalevTq1bt2aJk2aRBcvXiR8YWUavV5PGzdupK1bt9Lo0aPJ0tLSiEkNJ6UPfvjhB7Prg2fPntG6devo1atXZrn/KdL7OdiwYQOtXbuWatWqlSX6gL8HskgfiDxt+pTQ0FDUrFkThQsXxvbt2/HmzRsEBwejY8eO6NatG+7cuYPo6GjMmjULOXLkwNy5c6HX60XHlo0kSejVqxeICIUKFTKLPtDr9Vi2bBlcXV3h6OiIn376CTVq1DDb9wCQvs+Bh4cHihQpAiJC69atce/ePdHxMy2t+z9z5kw4Ojpi3LhxZv0eUOLnQJELV4aGhtLo0aMpODiYKlasSE2aNKF8+fJRUlISXb58mYKDgykmJoYmTpxI33zzTep0PFMHgEaMGEG//fYb/fzzz3Tp0iXavXs3VaxYkRo1apQl++C///6j/v3708mTJ6l79+7066+/koeHR+p7IKvv/5ekpw+6du1K27Zto6FDh1J0dDRNmDCBRo4cqZyj2AxIy/4/f/6ckpOTKTk5mQ4fPqyYISG5mPTnQHBx+6z4+Hi0aNECtra2KFmyJHLnzo18+fKhdu3amDZtGu7evSs6oqwkScKIESNARFiwYAGAt32we/du9OjRI8v1wfPnzzFw4ECo1WqULFkSR44c+eg1WXn/0yq9ffDq1SuMGjUKWq0WhQsXxp49ewQll0da9j8iIgLFixdHjhw5cOPGDdGRZfepPnB3dwcRYezYsYr9HCi2uCQnJyNbtmwYMWIEYmNj8fTpU0RHRyMhIUF0NNlJkoTRo0eDiDB//vxP/jyr9EHK4nseHh6ws7PD7NmzkZiY+NXfySr7n1Hp7YPLly+jTp06ICL4+vri0aNHRkpqGF/b//DwcBQrVgyenp64deuWoJSG9W4f3LlzBxqNJvVAVIkUW1wOHjwIIsLJkydFRzEoSZIwduxYEBF+//130XEM6tKlS6hduzaICB07dlTcEuFZjSRJ+PPPP+Hh4QFbW1vMnDnzq4XclIWFhaFo0aLIlSsXbt++LTqOwTVp0gR169YVHeOzFFtcBgwYgNy5c6euBpoVSZKE8ePHg4gwZ84c0XEMJiYmBiNGjIBGo0GRIkWwd+9e0ZHMyosXLzB48GCo1WqUKFEChw8fFh3JYJ48eYLChQsjd+7cuHPnjug4BrV8+XKo1WqEh4eLjvJJiiwuycnJyJ49O4YNGyY6ikFNnDgRRIRZs2aJjmIQkiRh48aNyJkzJ6ytrTFt2jTEx8eLjmW2zp8/j6pVq4KI8M033yAsLEx0JIN4/PgxChUqBC8vrywxc+5znj59Co1Gg0WLFomO8kmKLC5HjhwBEeH48eOioxjM5MmTQUT49ddfRUcxiOvXr6NRo0YgIrRt2zZLf8hNiV6vx/Lly+Hq6goHBwfMmzcPSUlJomPJLjQ0FAULFkSePHlw//590XEMplGjRmjQoIHoGJ+kyOIyaNAg5MyZU1FztuX0448/gojwyy+/iI4iu9evX2P8+PHQ6XTInz8/goKCREdinxAVFYU+ffpApVKhbNmyOHHihOhIsnv06BEKFCiAvHnz4sGDB6LjGMSSJUugVqsRGRkpOspHFFdc9Ho9PD09MWTIENFRDOKnn34CEWHatGmio8hu27ZtyJMnDywtLTFp0iTExcWJjsS+4tSpUyhfvjyICL169cLTp09FR5LVw4cPkS9fPuTPnx8PHz4UHUd2kZGR0Gg0WLp0qegoH1Fccfn3339BRPj3339FR5Hdzz//DCLC1KlTRUeR1Z07d9CyZUsQEZo2bZplp4JmVcnJyViwYAGcnJzg4uKCpUuXZqlRg/v37yNv3rwoUKCAyU/J/pQGDRqgUaNGomN8RHHFZejQofD09MxSb24AmDFjBogIU6ZMER1FNm/evMGUKVNgZWWF3LlzIzAwMEvP7svqIiIi0KNHDxARKleunPqM9qzg3r17yJMnDwoWLJjlpsAvWrQIGo0GUVFRoqO8R1HFRa/XI1euXBg0aJDoKLKaOXMmiAg//PCD6Ciy2bVrFwoWLAitVosxY8YgNjZWdCQmk6NHj6JUqVJQqVQYMGAAnj9/LjqSLO7evQsvLy8ULlwYjx8/Fh1HNuHh4VCr1Vi+fLnoKO9RVHE5fvw4iChLzcOfPXs2iAjff/99ljiqf/jwIby9vUFEqFevHq5evSo6EjOAxMREzJkzB3Z2dsiWLRvWrFmTJd6/d+7cQa5cuVCkSBE8efJEdBzZ1K1bF02aNBEd4z2KKi7Dhw9H9uzZkZycLDqKLH777TcQEcaPH2/yH8yEhATMmDEDtra2yJEjB9avX2/y+8S+7vHjx+jUqROICLVq1UJISIjoSJl2+/Zt5MyZE0WLFs0y9/osWLAAWq0Wz549Ex0llWKKiyRJ8PLyQv/+/UVHkcW8efNARBgzZozJfwkfPHgQxYoVg0ajwdChQ/Hy5UvRkZiR7du3D0WKFIFGo8Hw4cMRExMjOlKm3Lp1C56enihevLhi73BPj7CwMKhUKqxcuVJ0lFSKKS6nTp0CEeHgwYOio2TaH3/8ASLCqFGjTLqwPHnyBF26dAERoUaNGrhw4YLoSEyghIQETJ8+HTY2NvD09MTff/9t0u/vGzduIEeOHChRogQiIiJEx8m02rVro3nz5qJjpFJMcRk5ciSyZctm8kNiCxcuBBFh+PDhJvvBS0pKwty5c+Hg4AB3d3esWrUqy83eYxn34MEDtGvXDkSEhg0b4vr166IjZdj169eRPXt2lCpVSpE3IqbHvHnzoNPpFDMBQxHFRZIk5M2bF3379hUdJVMWL14MIsLQoUNNtrAcO3YMZcqUgUqlQr9+/RAdHS06ElOo4OBgFChQADqdDuPGjTPZGYNXr16Fh4cHSpcubdI3kT5+/BhEhDVr1oiOAkAhxeXMmTMgIuzbt090lAxbunQpiAiDBw82ycISGRmJnj17gohQqVIlnDlzRnQkZgLevHmDyZMnw9LSEl5eXtiyZYtJvv+vXLmCbNmyoUyZMoq7XyQ9atSogZYtW4qOAUAhxWXMmDFwc3Mz2QX0VqxYASLCwIEDTe6DlZycjEWLFsHZ2RnOzs5YvHixyQ9NMuO7ffs2mjVrBiJC8+bNTXK5+8uXL8Pd3R3lypVT1Kyr9Jg7dy4sLCzw4sUL0VHEFxdJkpA/f374+fmJjpIhK1euTB1CMrXCcubMGVSsWBFEhO+++87kx5yZWJIkYcuWLfDy8oKlpSUmT56MN2/eiI6VLiEhIXBzc0P58uVNckj40aNHICKsW7dOdBTxxeX8+fMgIpN81vfq1auhUqnQt29fk7rgHR0djb59+0KlUqF06dI4duyY6EgsC4mNjcXYsWOh0+lQoEABBAcHi46ULhcvXoSrqysqVKigmIvj6VGtWjW0adNGdAzxxWXcuHFwdXU1ucevrlu3DiqVCr179zaZwqLX67Fy5Uq4ubnB3t4ec+fONdmhSKZ8165dQ/369UFEaN++vUkte3/hwgW4uLigUqVKihhiSo85c+bA0tJS+P1oQouLJEkoWLAgevXqJTJGuv35559Qq9Xo1auXyRSWCxcuoEaNGiAidOnSJUstfcGUS5IkbNiwATly5ICNjQ2mT5+OhIQE0bHS5Pz583B2dkaVKlVMqsA8ePAARIS//vpLaA6hxeXChQsgIuzevVtkjHRZv3491Go1evbsaRKF5eXLlxg6dCg0Gg2KFSuGAwcOiI7EzNDLly8xbNgwaDQaFC1a1GTeh+fOnYOTkxOqVq0q/EwgPapUqYJ27doJzSC0uEyYMAHOzs4mMyT2999/Q61Wo0ePHoovLJIkYf369alHjDNmzDCZI0aWdYWEhKBmzZogInTu3NkkzqDPnj0LR0dHVK9e3WSWvZk5cyasrKzw6tUrYRmEFRdJklC4cGH07NlTVIR02bRpEzQaDbp166b4qbpXr15FvXr1QETw9vbOkk/gY6ZLkiSsXr0a7u7usLe3x2+//ab4a3+nT5+Gg4MDatasKfQLO63u3bsHIsLff/8tLIOw4hISEgIiws6dO0VFSLOAgABoNBp07dpV0YXl1atXGD16NLRaLQoWLGhSw43M/ERHR6N///6psxaV/vTZkydPwsHBAbVq1TKJAlOxYkV4e3sLa19Ycfnhhx/g5OSk+KGazZs3Q6vVonPnzoo9upIkCYGBgcidOzesrKzw448/mtz9Bcx8nT17FpUrVwYR4dtvv1X0IpLHjx+Hvb096tSpo/jlbmbMmAFra2thOYUVl2LFiqFHjx6imk+TrVu3QqvVomPHjootLLdu3ULTpk1BRGjZsqVJ3hnNmF6vx5IlS+Ds7AwnJycsXLhQsaMEx44dg52dHerVq4fXr1+LjvNZd+7cARFh06ZNQtoXUlyuXLkCIsKOHTtENJ8m27dvh06ng6+vryILS1xcHH744QdYWloiT5482LZtm+hIjGXa06dP0atXLxARKlasiNOnT4uO9ElHjx6Fra0t6tevr+gCU758eXTo0EFI20KKy+TJk+Hg4ID4+HgRzX/Vjh07oNPp4O3trciZbEFBQciXLx90Oh0mTJig6Dc3Yxlx/PhxlC1bFiqVCn369FHkWl9HjhyBra0tGjZsiLi4ONFxPinl+TsiviOEFJeSJUvim2++EdH0V+3cuRMWFhZo166d4grL/fv30aZNGxARGjVqhBs3boiOxJjBJCUl4ffff4eDgwPc3NywYsUKxd0CcOjQIdjY2KBx48aKvM5569YtEBECAwON3rbRi8u1a9dARIocxtm1axcsLS3Rpk0bRU00iI+Px7Rp02BtbY2cOXNi06ZNJrdIJmMZFRYWhm+++QZEhOrVq+O///4THek9Bw8ehLW1NZo2barIAlO2bFl06tTJ6O0avbj8+OOPsLe3V9x/wj///ANLS0u0atVKUYVl7969KFy4MLRaLUaOHGkyN3ExJrdDhw6hePHiUKvVGDx4sKKWZNm/fz+srKzQrFkzxQ33//TTT7C1tTX60J3Ri0vp0qXRpUsXYzf7RXv37oWVlRVatGihmDdGaGgoOnToACJC7dq1cfnyZdGRGBMuMTERM2fOhK2tLbJnz44///xTMWfxSvweAYAbN26AiLBlyxajtmvU4pKyk5s3bzZms1+0b98+WFlZoXnz5op4QyQmJmLWrFmws7NDtmzZsHbtWsV8eBhTikePHsHHxwdEhLp16+LKlSuiIwFQ7ghIqVKljH5Qb9TiMm3aNCGnZ59z4MABRY2VHj58GCVLloRarcagQYNM8lkSjBnTP//8g0KFCkGr1WLUqFGKuHN+9+7dirt2K+JyhFGLS9myZdGxY0djNvlZSprlER4ejm7duoGIUKVKFZw/f15oHsZMSXx8PKZOnQorKyvkypULAQEBws/2g4ODFTXr9OrVq0afSGW04pIyJS4gIMBYTX7W4cOHYWNjI3x+enJyMv744w84OjrC1dUVy5YtU9xUS8ZMxd27d9GqVSsQEZo0aYKbN28KzRMUFKSo++VKlCiBbt26Ga09oxUXkTfzvCvlztoGDRoIzXLixAmUK1cu9WmWUVFRwrIwlpVs374defPmhYWFBSZOnCj0AFJJK30Y++Z1oxWXChUqwNfX11jNfZIS1gSKiopC7969QUQoV64cTp48KSQHY1nZ69ev8f3338PCwgL58uUTutSUUtYovHz5MogIQUFBRmnPKMVF9AJqgPjVTPV6PZYtWwZXV1c4Ojrijz/+UOzCfIxlFTdu3EDjxo1BRGjdujXu3bsnJEfK6uqdOnUSWmCMuWCwUYrLr7/+KnTp5zNnzsDe3h61a9cWkuHFixeoWrUqiAjdu3dHeHi40TMwZq4kSYK/vz9y5swJa2trrF69WkiOwMDA1OdCiZpwMHHiRKM96kQFACSzxMTEr75GkiRq164d7dq1S+7m09Q+EVHTpk3pwIEDsrdPRDR58mTKli0b/e9///vqay0sLAySgTFz9/PPP9PLly/J3t6e/Pz8yMnJ6bOvNcTnMK3fRY0aNaLDhw8La79t27YUHBwsa9sGKS5fExkZSWPHjqWZM2eSq6ursZsnIiK9Xk/Lli2jvn37GqyN/fv30927d6l3794Ga4Mx9mUAKCwsjGbPnk2tW7emOnXqiI70noiICLpw4QI1adJESPtDhgyhH3/8kRwdHWXdrlGLCwBas2YN3bp1iyZMmEA2NjbGavojtWvXpiNHjhi8neXLl1PdunWpYMGCBm+LMfZ5AGj58uVkZWVF3bp1Ex0nVZkyZejixYtC2r558yZdv36dWrduLfu2jVZcAFCfPn2oV69eVLlyZVKpVMZo9pMiIiIoJCSEGjVqZJT2mjVrRjt37iS1Wm2U9hhjnxcQEEAAyNfXV3QUmjRpEo0ePZpsbW2N3nZycjK1bNmSdu/ebZDtG+3brk+fPjRt2jSqUqWK0MICgJo2bWq0wkJEtHPnTmrVqpXR2mOMfZ6Pjw9FRETQjRs3hOY4dOgQlSxZUlhh8fb2lv06y7uMUlyOHj1Kffr0IXd3d2M090WjR4+mY8eOGbVNtVpN8+fPp19//ZUEXOJijH1g4MCBNGrUKGGfx927d9OJEyeEnD29evWKvv32W/rzzz8NOppi8OICgGbNmkUVKlQwdFNf9ffff1OjRo2EXOvJnz8/Va9enaZMmUKxsbFGb58x9r5t27ZRy5YtjdomAPrll1/o2bNnNG7cOKO2TUQUHR1NAwcOpBUrVpC9vb1B2zL4NRdvb28KCAgQOhQWGxtL8+bNo3z58lHnzp2F5SAievToEc2bN4/Kly9PnTp1EtovjJm7kydPkrOzMxUpUsTgbcXHx1P//v1p9OjRVLRoUYO396Hk5GRq3749bd261SjXfw1aXI4fP06SJFHNmjUN1cRnAaCrV6/S9u3b6c2bN9S9e3fFzNgCQEePHqWNGzfSggULRMdhzKxVqFCBzp07Z9A2wsPDadSoUbRo0SKys7MzaFufAoCaN29OQUFBpNFojNKmQYqLXq+ny5cv06pVq2ju3Llybz5N7Y8ZM4ZKlChBbdq0IWdnZ0WeIdy5c4eCg4Np0KBBoqMwZrYSExPpt99+ozFjxsi+bUmSaNeuXbR//36aOXOm0b7YUyQnJ1NycjINHjyYpk+fbtT7CrWG2OjAgQMpV65cNHHiRHr27NkXX2uInf3f//5Ho0ePpmzZshEAio6ONmr7RPTV/SYicnJyEj5jhbGsLC2fQyKihw8fGqT9nj17UtOmTWnChAn04sWLL77WEN9FQ4YMIZVKRQMHDiSiL/eH3O0b5MwlKioqzWN6Li4ucjcvvH0i+mJBM1YGxsyd6M/h06dP03y2Yoj2nz17luZRG9nbN/jqZQDmzJkDrVaLggULYvfu3cZo8j1nzpyBg4MDatWqJeQxqJIkIU+ePOjbt6/R22aMvfX48WOoVCphC1cGBAQIW7gyOjoa/fv3h0qlQunSpfH48WODt2m057lcvXoV9erVAxHB29sbDx8+NFbTAMQvuT9ixAhky5aNl9lnTJD58+dDp9MhOjra6G2nLLnfuXNnoy65L0kSVq9eDXd3d9jb2+O3334zWvtGKy7A2x1dv349smfPDltbW8yYMcMoSz+nEPmwsJMnT4KIcPDgQaO2yxh7q3bt2mjWrJnR2xX1sLCQkBDUrFkTRITOnTsb5WzlXUYtLilevnyJoUOHQqPRoFixYkb9wk15zHH9+vWNWmAkSULu3LkxYMAAo7XJGHsrLCwMKpUKK1asMGq7Ih5z/PLlSwwbNgwajQZFixbF/v37jdLuh4QUlxQXLlxAjRo1QETo0qULnjx5YpR2jxw5AltbWzRs2NCoz9ceNmwYsmfPzkNjjBnZggULoNVq8ezZM6O1uWPHDuh0Onh7eyMxMdHg7UmShA0bNiBHjhywsbHBL7/8YtSRoQ8JLS7A28f/rlq1Cu7u7nBwcMDcuXONUuEPHToEGxsbNG7cGG/evDF4e8DbYTkiwuHDh43SHmPsrbp166Jx48ZGa2/nzp2wsLBAu3btjFJYrl27hvr164OI0L59ezx48MDgbX6N8OKSIjo6Gv369YNKpUKZMmVw7Ngxg7d58OBBWFtbo2nTpkYpMHq9Hjlz5sSgQYMM3hZj7K3w8HCo1WosW7bMKO3t2rULlpaWaNOmjcHPHGJjYzF27FjodDoUKFAAu3btMmh76aGY4pLi9OnTqFixIogIPXv2RGRkpEHb279/P6ysrNCsWTPEx8cbtC0AGDx4MDw9PaHX6w3eFmMMWLRoETQaDZ4+fWrwtv755x9YWlqiVatWBi0skiRh8+bN8PLygqWlJaZMmWK0EZi0UlxxAYDk5GQsXrwYzs7OcHZ2xqJFiwx6nWLv3r2wsrJCixYtDF5gjh49CiLCv//+a9B2GGNvNWjQAA0bNjR4O8b6Hrl9+zaaNWsGIkKLFi1w584dg7WVGYosLikiIyPRs2dPEBEqVqyIM2fOGKwtYx1x6PV65MiRA0OGDDFYG4yxtyIjI6FWq7F48WKDtrNv3z5YWVmhefPmBissb968waRJk2BpaQkvLy9s3brV6Ddjpoeii0uKf//9F6VLl4ZKpUK/fv0MdhPU7t27jTJWOnDgQOTKlYuHxhgzsKVLl0KtViMiIsJgbRw4cMDg12537tyJ/PnzQ6fTYdy4cUJuBE8vkyguAJCUlIS5c+fC3t4ebm5uWLlypUG+nIODgw0+y+Pw4cMgIhw/ftwg22eMvdWoUSPUr1/fYNs39KzT+/fvo23btiAiNGjQANeuXZO9DUMxmeKS4smTJ+jSpQuICDVq1MCFCxdkbyMoKMig89OTk5Ph4eGB4cOHy75txthbUVFR0Gg0WLhwoUG2f/jwYdjY2BjkfrmEhAT8/PPPsLa2hqenJ/7++29FD4F9iskVlxQHDhxAsWLFoNFoMHToULx8+VLW7Rv6ztr+/fvDy8vL5N4wjJmK5cuXQ6VSITw8XPZtp6z00aBBA9lX+ti3bx+KFCkCjUaD4cOHIyYmRtbtG4vJFhfgbXWfMWMGbGxskCNHDqxfv17WL2tDrgl04MABEBFOnTol63YZY281bdoUderUkX27hlqj8PHjx+jUqROICLVq1UJISIhs2xbBpItLiocPH8Lb2xtEhHr16uHq1auybTtlNdNOnTrJWmCSk5Ph7u6OkSNHyrZNxthbz549g1arxR9//CHrdg2xunpiYiJmz54NOzs7ZMuWDWvWrMkSIxpZorik2L17NwoWLAitVosxY8bI9p8fGBgIjUaDLl26yHq/TZ8+fZAnT54s8UZiTElWrlwJlUol63qFJ0+ehL29PWrXri3bd8vRo0dRqlQpqNVqDBgwAM+fP5dlu0qQpYoL8HYu+I8//ggrKyvkzp0bgYGBsnx5+/v7Q6PRoFu3brIVmH379oGIDHr/DmPmqHnz5qhVq5Zs2zt16hQcHBxQs2ZNWR44GBERgR49eoCIULlyZZw7d06GlMqS5YpLijt37qBly5YgIjRt2hS3bt3K9DY3btwIjUaDHj16yFJgkpKS4ObmhtGjR2d6W4yxt54/fw6dTofff/9dlu2dOXMGjo6OqF69eqYvricnJ2PBggVwcnKCi4sLli5dmmXvd8uyxSXFtm3bkCdPHlhaWuKHH37I9JTBDRs2QK1Wo2fPnrK8KXr37o38+fPz0BhjMlmzZg2ICKGhoZne1rlz5+Dk5IRq1aplekbqqVOnUKFCBRAR/ve//xllrTORsnxxAYDXr19jwoQJ0Ol0yJcvH4KCgjK1vb/++gtqtRq9evXKdIH5559/QERZ8rSYMRFatmyJ6tWrZ3o758+fh7OzM6pUqYIXL15keDtRUVHw8/ODSqVCuXLlcOLEiUxnMwVmUVxS3LhxA40aNQIRoU2bNrh//36Gt7Vu3TqoVCr07t07UwUmMTERLi4uGDduXIa3wRh768WLF7CwsMBvv/2Wqe1cuHABLi4uqFy5coYLi16vx/Lly+Hq6gpHR0fMnz/frB4UaFbFBXi7VPWmTZuQM2dOWFtbY9q0aRleaG7NmjVQqVTo06dPpgpMr169ULBgQR4aYyyT1q1bByLCw4cPM7yNixcvwtXVFRUrVszw7K3//vsP1apVAxGhW7duBrmRU+nMrrikiImJwciRI6HValG4cGHs3bs3Q9tZtWpV6oKaGS0Ou3btAhEZZCkbxsxJmzZtULVq1Qz/fkhICNzc3FC+fPkMLZD74sULDBo0CGq1GiVKlDDrp86abXFJcfnyZdSuXRtEhA4dOmToIuCKFStARBgwYECGCkxiYiKcnZ0xYcKEdP8uY+ytly9fwtLSErNnz87Q71++fBnu7u4oV64cnj17lq7flSQJ69atg4eHB+zs7DBr1iyjPN5Yycy+uABv3xhr165FtmzZMvzGWLZsGYgIgwcPzlCB+fbbb1G4cGEeGmMsg/766y8QUYaupV65cgXZsmVDmTJlEBUVla7fvXz5MurUqZN6gPro0aN0t58VcXF5x/Pnz1NPaUuWLJnuU9olS5aAiDBkyJB0F4mdO3eCiEx+PSHGRGnXrh0qV66c7t+7evUqPDw8ULp06XRND3716tV7Q+t79uxJd9tZGReXTzh//jyqVKmSoYtxixYtAhFh+PDh6SowCQkJcHR0xMSJEzMSmTGz9urVK1hZWeHXX39N1+9dv34d2bNnR6lSpdJcWOScFJSVcXH5DL1ej2XLlqVOI/zjjz/SPI3wjz/+ABFh5MiR6Sow3bt3R7FixTIamTGz9ffff4OIcPfu3TT/zo0bN5AjRw6UKFECkZGRaf6dxo0bg4jQunVr3Lt3L4OJsz4uLl8RFRWF3r17p/sGqHnz5oGIMGbMmDQXmO3bt4OIcPny5cxEZszseHt7o0KFCml+/c2bN+Hp6YnixYun6RHIKTdiW1hYIF++fNixY0dm4poFLi5pdPLkSZQvXz516Ya0XPSbO3cuiAjjxo1LU4GJj4+Hvb09Jk+eLEdkxsxCbGwsrK2t8csvv6Tp9bdu3ULOnDlRtGjRNA15b9u2DXnz5oWFhYUsS0iZCy4u6ZCcnIw//vgDjo6OcHFxwbJly7568+ScOXNARJgwYUKaCkzXrl1RokQJuSIzluVt2rQJRITbt29/9bW3b99Grly5UKRIka8ux3/37t3UxW+bNGmCmzdvyhXZLHBxyYDw8HB0794dRISqVavi/PnzX3z9rFmzQET44YcfvrrtrVu3gohkfeAZY1lZhw4dUK5cua++7u7du8idOzcKFy78xcISHx+PqVOnwsrKCrly5UJAQADfIpABXFwy4ciRIyhZsiTUajUGDhz4xaUiZsyYASL66pDXmzdvYGdnhx9//FHmtIxlPa9fv4aNjQ1+/vnnL77u3r17yJMnDwoWLPjFG6XffeDg6NGjZXl2i7ni4pJJHz6idO3atZ89ypk+fTqI6KuFo3PnzihdurQh4jKWpQQGBoKIvjhkdf/+feTNmxcFChT47A2Ojx49go+PD4gIdevWxZUrVwwV2WxwcZFJaGgoOnbsCCJC7dq1cenSpU++btq0aSAiTJs27bPb2rx5M4gIN27cMFRcxrKETp06oUyZMp/9+YMHD5AvXz7kz5//k4tZJiYm4tdff4WtrS2yZ8+Ov/76i4fAZMLFRWZ79+5FkSJFoNFoMGLEiE8+ue7HH38EEWH69Omf3EZcXBxsbW3x008/GTouYyYr5XMyderUT/780aNHyJ8/P/Lly4cHDx589PODBw+iePHiUKvVGDJkSKae2cI+xsXFAOLj4/Hzzz/D2toanp6e2Lhx40dHQ5MnTwYRYcaMGZ/cRseOHVG2bFljxGXMJG3ZsgVEhOvXr3/0s9DQUBQoUAB58+b9aK2xsLAwdO3aFUSE6tWr82rkBsLFxYDu37+Ptm3bgojQsGHDjz4EEydOBBFh1qxZH/2uv78/iAi3bt0yVlzGTEqXLl1QsmTJj/798ePHKFSoELy8vN67gz4pKQm///47HBwc4ObmhpUrV2bZ59crARcXIwgKCkL+/Pmh0+kwfvx4vH79GsDbNYomTJgAIsKcOXPe+52UWTCfGzpjzJy9efMG9vb2mDJlynv//uTJExQuXBi5c+fGnTt3Uv/9+PHjKFu2LFQqFfr27ZvuJfVZ+nFxMZK4uDhMmjQJlpaWyJMnD7Zu3QpJkiBJEsaNGwciwty5c9/7HR8fH5QvX15QYsaUa9u2bSCi92Z1hYWFoUiRIsiVK1fqDZWRkZH47rvvQESoWLEiTp8+LSqy2eHiYmS3bt1Cs2bNQERo0aIF7ty5A0mSMHr0aBAR5s+fn/rajRs3gojeOwJjjAHdunVD8eLFU/8eHh6OYsWKIWfOnLh16xaSk5OxePFiODs7w9nZGYsWLTKr59crARcXASRJwubNm5E7d25YWVlhypQpiIuLw8iRI0FE+OOPPwD8/2XEP3fRnzFzFB8fDwcHh9QVLyIiIlC8eHHkyJEDN2/exNmzZ1GpUiUQEXr27JnmFY+ZvLi4CBQbG4sxY8ZAq9WiYMGCCA4OxvDhw0FEWLRoEQCgfv36cHNzg4uLC3Q6HVxcXPDdd9/h3LlzgtMzZjznzp3Dd999BxcXF2g0GhAR2rVrh3379qFEiRLIkSMHTp06hX79+kGlUqF06dL4999/Rcc2a1xcFODq1auoX79+6gcmZYy4Vq1aIKKP/mi1WhAR/Pz8kJSUJDo+YwaTlJQEPz+/9973KX/UajWICFZWVpg6dSrc3d1hb2+PuXPn8udCAVQAQEw4ALRx40YaPnw4vXjxghwcHCgiIuKLv6NSqah37960ZMkSI6VkzLj69OlDy5Yto7R8TXXp0oVmzZpFOXLkMEIy9jVcXBQmJiaG+vXrR+vXr0/z75w7d47Kly9vwFSMGd/58+epQoUKaX49fw6URS06AHufg4MDWVlZkUajSdPrtVotLVy40MCpGDO+BQsWkFarTdNr+XOgPHzmokCurq4UHR2d5te7uLjQs2fPDJiIMePjz4Fp4+KiQBYWFpSUlJTm1+t0OkpMTDRgIsaMjz8Hpo2HxRTI3t7eoK9nzBTw58C0cXFRoLZt26ZrrLldu3YGTsSY8fHnwLTxsJgC8SwZxvhzYOr4zEWBypcvT35+fqRSqb74OpVKRX5+fvyBYlkSfw5MGxcXhVqwYAH17t2biOijoYGUv/fu3ZsWLFhg9GyMGQt/DkwXD4sp3Pnz52nhwoXk7+9PMTEx5ODgQL6+vtS/f38+UmNmgz8HpoeLi4lIGX/mcWVmzvhzYDp4WIwxxpjsuLgwxhiTHRcXxhhjsuPiwhhjTHZcXBhjjMmOiwtjjDHZcXFhjDEmOy4ujDHGZMfFhTHGmOy4uDDGGJMdFxfGGGOy4+LCGGNMdlxcGGOMyY6LC2OMMdlxcWGMMSY7Li6MMcZkx8WFMcaY7Li4MMYYkx0XF8YYY7Lj4sIYY0x2WtEB2Jfp9Xp6+PAhHTlyhIiIgoODKSEhgYoXL06Ojo6C0zFmeCmfgStXrtDp06eJiCgkJIQKFCjAnwEFUwGA6BDsYwAoJCSEZs6cSfv27SMA5OjoSAAoJiaGPDw8qFevXtSzZ09ycHAQHZcx2X34GSAicnJyoqSkJIqJiaEcOXLwZ0DBuLgokCRJtGnTJhoxYgR5eXnRgAEDqEqVKmRra0uSJNHz588pODiYli1bRsWKFaPFixdTzpw5RcdmTDb8GcgCwBRn586dcHNzQ79+/RAVFQVJkrB27VoUK1YMZcuWxeXLlyFJEq5du4ZatWqhefPmePHihejYjMmGPwOmjy/oK8zTp09p7NixVKdOHZoxYwa5uLiQSqWi6OhounbtGl2/fp3i4+NJpVJRkSJFaMWKFXT37l1atmyZ6OiMyYI/A1kDFxeF2bp1K4WFhdHEiRPJzs6OVCrVZ1+rUqmoYMGCNGzYMFqxYgU9e/bMiEkZMwz+DGQNXFwURK/X086dO6ly5crk5eVF4eHhFBYWRmFhYRQTE0NEby9yRkVFpf57REQENW3alOLj4+nChQtid4CxTOLPQNbBU5EVJD4+nu7cuUOtWrWi5cuX0+zZs1N/FhcXR0RECQkJ1LVrV9Jq3/7Xubi4UFBQEOXKlYtu3rxJDRo0EJKdMTnwZyDr4OKiIHq9nhISEsjOzo5iY2MpIiLik69799Q/OTmZiIisra1TP3yMmSr+DGQdXFwUxNLSkpydnSk0NJSaNWtGffv2Tf3ZpUuX6NixY6TRaKhdu3bk5uZGRER2dnak0+koKiqKPDw8REVnTBb8GchCRE9XY+/r168fypUrh5cvX0KSpNQ/c+fOBRHBysoKZ8+efe9n58+fh6enJy5evCg6PmOZxp+BrIEv6CuMl5cXXblyhXbs2EFEb2fDfGq2TMq/Jycn07Jly6hUqVJUpEgRY8dlTHYdOnSgu3fvpuszsHTpUipatCh/BhSEi4tCPHjwgNq1a0fjxo0jFxcXmjRpEl28eJHwhQUU9Ho9bdy4kbZu3UqjR48mS0tLIyZmzDCqV69OrVu3TvNn4O+//6a1a9fS2bNnaf369SRJkhHTss/h4iJYYmIiTZ8+nYoVK0anT5+mv//+m86cOUM5cuSgjh07UlBQEMXHx1PhwoWpY8eO5OvrS87OzvT8+XOaM2cODRkyhEaNGkV169YVvSuMycLCwoI6dOhA9+/fpw4dOnzxMzB37lwaM2YMjR07llq0aEHfffcd1a5dmy5evCh6N8wery0m0P79+2nAgAF0+/ZtGjJkCE2ePJns7e2JiCg0NJRGjx5N27Zto+rVq1Pjxo0pX758lJSURJcvX6bg4GAKCwujyMhI+uabb2jVqlWk0WgE7xFjmXf27Flq2LAhFSxYkPLly0f79++nihUrUqNGjT76DMTExNDEiRPpm2++Ia1WSwcPHqQBAwbQzZs3adCgQTRlyhRe1FIUsZd8zNPjx4/RqVMnEBFq1aqFkJCQT77uxo0bqa8pWbIkcufOjXz58qF27dqYNm0a7t69i/Xr10OtVqNnz57Q6/VG3hPG5HXu3Dk4OTmhatWqePnyJeLj47F792706NHjvc+AlZUVKlSogLt37360jYSEBMyYMQM2NjbIkSMH1q9fD0mSBOyNeePiYkSJiYmYPXs27OzskC1bNqxZs+aLb/rZs2fD0tISL168QGxsLJ4+fYro6GgkJCS897o///wTarUavXr14gLDTNb58+fh7OyMypUrf7QIpSRJ730GRo8eDRcXFyQmJn52ew8fPoS3tzeICPXq1cPVq1cNvQvsHVxcjOTIkSMoVaoU1Go1BgwYgOfPn3/1d6pWrYrWrVunaftr166FSqVC7969ucAwk3PhwgW4uLigYsWKafpsnDt3DkSEf/7556uv3b17NwoWLAitVovRo0fj1atXMiRmX8PFxcAiIiLQo0cPEBEqV66Mc+fOpen3Hj58CCLCunXr0tzW6tWroVKp0KdPHy4wzGRcvHgRrq6uqFChAqKjo9P0O5IkIX/+/Ojdu3eaXv/mzRv8+OOPsLKyQu7cuREYGMhDZQbGxcVAkpOTsWDBAjg5OcHFxQVLly5N1xf+b7/9BgsLi3Q/o2LlypVQqVTo168ff3iY4l26dAlubm4oX758mgtLitGjR8PNzQ1JSUlp/p07d+6gZcuWICI0bdoUt27dSm9klkZcXAzg1KlTqFChAogI//vf//D06dN0b6NGjRpo2bJlhtpfvnw5iAgDBw7kAsMU6/Lly3B3d0fZsmXx7NmzdP/+mTNnQETYt29fun9327ZtyJMnDywtLfHDDz8gLi4u3dtgX8bFRUZRUVHw8/ODSqVCuXLlcOLEiQxtJzQ0FESE1atXZzjLkiVLQEQYPHgwFximOFeuXEG2bNlQpkwZREVFZWgbkiQhb9686NOnT4Z+//Xr15gwYQIsLCyQL18+BAUFZWg77NO4uMhAr9dj+fLlcHV1haOjI+bPn4/k5OQMb+/333+HTqdL04XNL1m8eDGICEOHDuUCwxTj2rVr8PDwQKlSpTJ0Vv+ukSNHwt3dPV1DYx+6ceMGGjVqBCJCmzZtcP/+/UxlYm9xccmk//77D9WqVQMRoVu3bggPD8/0NlOeCS6HBQsWgIgwfPhwLjBMuOvXryN79uwoWbIkIiMjM729U6dOgYhw4MCBTG1HkiRs2rQJOXPmhLW1NaZNm4b4+PhM5zNnXFwy6MWLFxg0aBDUajVKlCiBw4cPy7LdJ0+eQKVSYeXKlbJsDwDmz58PIsLIkSO5wDBhbty4gRw5cqB48eKIiIiQZZuSJMHLywv9+vWTZXsxMTEYOXIktFotChcujL1798qyXXPExSWdJEnCunXr4OHhATs7O8yaNeuLN3Kl1x9//AGtVpuhC5xf8vvvv4OIMGbMGC4wzOhu3rwJT09PFCtWTJaz+3cNHz4cHh4emRqK/tDly5dRu3ZtEBE6dOiA0NBQ2bZtLri4pMPly5dRp04dg77h6tSpgyZNmsi+XQCYM2cOiAjjxo3jAsOM5tatW8iZMyeKFi2KsLAw2bd//PhxEBEOHTok63YNfSCZ1XFxSYNXr169d6q8Z88eg7QTHh4OlUqF5cuXG2T7wNslZYgI33//PRcYZnB37txBrly5ULhwYTx58sQgbej1euTKlQsDBw40yPafP3+eOgResmRJ2YbAszouLl9g7It8CxcuhEajyfQMmq/59ddfQUSYNGmSQdth5u3u3bvw8vJCoUKF8PjxY4O2NWTIEOTIkcOgK1OcP38eVatWlXXyTlbGxeUzPpyeeO/ePYO3Wb9+fTRq1Mjg7QDAL7/8AiLC5MmTjdIeMy/37t1Dnjx5ULBgQaNcr/j3339BRDh69KhB25H7toOsjIvLB0TdWBUREQG1Wo0lS5YYpT0A+Pnnn0FEmDp1qtHaZFnf/fv3kTdvXhQoUACPHj0ySpt6vR6enp4YPHiwUdqT64bprIyLyzu2bduGvHnzwsLCwuhLQixevBgajUaWuf/pMXXqVBARpk2bZtR2Wdb08OFD5MuXD/ny5cPDhw+N2vagQYPg6elp1EVbT548ifLly6cu9ZTR1QayIi4ueDs2LHoxu4YNG6JBgwZGbxcApkyZAiLC9OnThbTPsoZHjx4hf/78yJs3r5C73I8cOQIiwrFjx4zabsoitY6OjhlapDarMuviopRluJ8+fQqNRoNFixYZve0UkyZNAhHh119/FZaBma7Q0FAUKFAAefLkMcr1yU9JTk5G9uzZMXToUCHtv/t4jSpVqqT58RpZldkWl3cfIDRmzBjExsYKy7Js2TKo1Wqhs08kScL3338PIsKsWbOE5WCm5/HjxyhUqBC8vLw++dhhYxowYABy5col9MzhyJEjKFmyZLoeDJgVmV1xeffRp3Xr1sWVK1dER0Ljxo1Rt25d0TEgSRLGjx8PIsKcOXNEx2Em4MmTJyhcuDBy5cqFO3fuiI6DgwcPgoiEX2BP7yPNsyKzKS4JCQmYMWMGbG1tkT17dvz111+K+M+OioqCRqPBggULREcB8LbAjBkzBkSEuXPnio7DFCwsLAxFihRBzpw5cfv2bdFxALwdGsuWLRtGjBghOgqAt8OFHTt2BBGhVq1auHTpkuhIRmMWxeXgwYMoVqwYNBoNhg4dipcvX4qOlGrFihVQqVQGWRYjoyRJwqhRo0BEmD9/vug4TIHCw8NRrFgxeHp64ubNm6LjvKdv377IkyePIg4eU+zbtw9FihSBRqPB8OHDERMTIzqSwWXp4vLkyRN06dIFRITq1avjwoULoiN9pFmzZqhdu7boGB+RJAkjRowAESnmrIopQ0REBIoXL44cOXLgxo0bouN8ZP/+/SAinD59WnSU9yQkJODnn3+GtbU1PD09sXHjRkUVQLllyeKSlJSEuXPnwsHBAW5ubli5cqUipwZGR0dDp9Nh3rx5oqN8kiRJGDp0KIhI6Ew2phyRkZEoWbIksmfPjuvXr4uO80lJSUlwc3PDqFGjREf5pPv376Nt27YgIjRs2FCx/ZhZWa64HDt2DGXKlIFKpULfvn1lX7peTqtXrwYRGXzdpcyQJAmDBw8GERl19QCmPE+fPkWpUqXg4eGBq1evio7zRX5+fsiXL5+izwx27tyJ/PnzQ6fTYdy4cXj9+rXoSLLKMsUlMjISPXv2BBGhYsWKijsl/pQWLVqgRo0aomN8lSRJGDhwIIgIy5YtEx2HCRAVFYXSpUsjW7Zsiphh+TV79uwBEeHs2bOio3xRXFwcJk2aBEtLS3h5eWHLli2KLojpYfLFJTk5GYsWLYKzszOcnZ2xaNEik1hI7vnz59DpdCYzI0uSJPTv3x8qlQorVqwQHYcZ0bNnz1C2bFm4u7vj8uXLouOkSVJSElxdXTFmzBjRUdLk9u3baNasGYgIzZs3V8S07swy6eJy5swZVKxYEUSEnj17Gn1drsxYu3YtiMhoC/vJQa/Xo2/fvlCpVFi1apXoOMwInj17hnLlysHNzQ0hISGi46TL//73PxQoUMBkzgQkScLmzZuRO3duWFpaYsqUKXjz5o3oWBlmksUlOjoa/fr1g0qlQunSpfHvv/+KjpRurVq1QrVq1UTHSDe9Xp+6GuyaNWtEx2EGFB0djQoVKsDV1RUXL14UHSfddu/eDSLC+fPnRUdJl9jYWIwdOxY6nQ4FChTArl27REfKEJMqLnq9HitXroSbmxvs7e0xd+5cJCUliY6Vbi9fvoSFhYXJ3gWv1+vxv//9DyqVCuvWrRMdhxnA8+fPUalSJbi4uChyCn9aJCYmwtnZGePHjxcdJUOuXbuG+vXrg4jQvn17PHjwQHSkdDGZ4nLhwgXUqFEDRIQuXboY7JGpxvDnn3+CiEzuzfIuvV6Pnj17Qq1W46+//hIdh8noxYsXqFy5MpydnU3uqP9DPXv2RKFChUxmaOxDkiRhw4YNyJEjB2xsbDB9+nQkJCSIjpUmii8uL1++xNChQ6HRaFCsWDEcOHBAdKRMa9u2LapUqSI6Rqbp9Xr06NEDarUaf//9t+g4TAYvX75E1apV4eTklCVW9Q0ODgYRmeSw3rtevnyJYcOGQaPRoGjRoibxPajY4iJJEtavX59asWfMmGEyFftLYmJiYGlpiZkzZ4qOIovk5GR069YNGo0GGzduFB2HZUJMTAyqVasGR0dHnDlzRnQcWSQkJMDJyQnff/+96CiyuHjxImrWrAkiQufOnRU9gqPI4nL16lXUq1cPRARvb2+jP9HOkDZs2AAiEvbMC0NITk5G165dodFo4O/vLzoOy4CYmBjUqFEDDg4OJnGPWHr06NEDRYoUMdmhsQ9JkoTVq1fD3d0d9vb2+O233xR57VlRxeXVq1cYPXo0tFotChYsiN27d4uOJLv27dujYsWKomPILjk5GZ07d4ZWq0VgYKDoOCwdXr16hVq1asHBwQEnT54UHUd2O3bsABFluRWJo6OjU+89U+KsWUUUF0mSEBgYiNy5c8PKygo//vijSc/v/pxXr17BysoKM2bMEB3FIJKSktCxY0dotVps2bJFdByWBrGxsahduzbs7e1x/Phx0XEMIj4+Hg4ODvjhhx9ERzGIs2fPonLlyiAifPvtt4iIiBAdCYACisutW7fQtGlTEBFatmyZJe5M/ZyNGzeCiLL0PiYlJcHX1xdarRbbtm0THYd9wevXr1G3bl3Y2dkZ/bnzxtatWzcUL15cdAyD0ev1WLJkCZydneHk5ISFCxcKX6lEWHGJi4vDDz/8AEtLS+TJk8csvoh8fHxQvnx50TEMLjExEd7e3tDpdNixY4foOOwTXr9+jfr168PW1hZHjx4VHcfgtm3bBiIyiXXRMuPp06fo1auXItZYFFJcgoKCkC9fPlhYWGDChAlZbjXQT4mNjU2dp24OEhMT0a5dO1hYWCAoKEh0HPaOuLg4NGjQALa2tjhy5IjoOEbx5s0b2NvbY8qUKaKjGMXx48dRtmxZqFQq9OnTR8jq8EYtLvfv30ebNm1ARGjUqJEiHzRkKP7+/iAi3Lp1S3QUo0lISEDbtm1hYWGB4OBg0XEY3haWRo0awcbGBocOHRIdx6i6dOmCkiVLio5hNElJSZg3b17qc61WrFhh1OdaGaW4xMfHY9q0abC2tkbOnDmxadOmLDMtMK06duyIsmXLio5hdAkJCWjdujUsLS2z5Ow/U/LmzRs0adIE1tbWOHjwoOg4RrdlyxYQEa5duyY6ilGFhYXhm2++SX0i73///WeUdo1SXPr16wetVouRI0eaxbOjPxQXFwdbW1v89NNPoqMIER8fj5YtW8LGxkYxM1nM0ciRI2FlZYX9+/eLjiJEXFwc7OzsMHXqVNFRhDh06BCKFy8OnU5nlNXYVQBAMluwYAE9fvyYwsLCaO7cuWRtbf3Z11pYWMjdvCIcP36cjh07RpGRkaTT6QgA2dnZ0ePHj2nq1Klkb2+f+tqs2AeJiYkf/duqVasoNDSUOnXqRIUKFUr996y4/0owdepUev36NY0dO5ZsbGy++Nqs+n/wqffhpzRu3JgOHTpk2DACfP/995SUlERqtZry589Ply5doufPn9OKFSs+eq3s7wFDVKwrV65AkiQkJSWhYcOGqeN8L1++xK+//mqIJhVn69atCAsLQ3JyMiRJSh0GjImJQYsWLQSnE6NFixaQJClLTwlVmsjISPj5+eHMmTNmNxSdVvHx8Vl2bby4uDjo9XrExcXh3r17kCQJN2/eNMqwqEHOXN715s0b6t+/P3Xt2pWWLl1KS5cupZMnT1LTpk0N2ayiJSUl0d27d6lIkSKioxjNpUuXqGTJkqRSqSguLo6ePn1KefLkER3LLACgtWvX0vXr16lDhw5Urlw50ZEUpXTp0hQSEiI6hlF5e3uTv78/qdVqg7Vh8OJCRBQXF0cXLlygKlWqkEajIbVaTZIkGbpZRbO2tqY3b96IjmE0lpaWlJCQkPp3Ozs7io2NFZjI/MTFxdGmTZsoLCyMxo0bJzqOIhw9epTc3NyoWLFioqMYFQBq2rQp/fPPPwZrw3Bl6x02NjZUvXp10mg0RERUvXp1YzSraOb2Zv7pp5/e+/vy5csFJTFfNjY29O2331KNGjXowIEDouMId/v2bVq/fr3ZfRaJiFQqFS1evJg2bNhguDaMcebyoaSkJNLpdMZuVlESExOz7EXUD0VGRpK7uzupVKr3/n3Lli3Url07QanMW/v27SkwMPCj/xNzkDJMeO/ePZo0aZJZ9kGKbt260dq1aw3SB0Y5c/mQTqej+Ph4EU0rhoWFBW3atEl0DKMoVqzYJ9+8vr6+AtIwIqLAwEDq3bu36BhGB4AGDBhAhQoVosmTJ5t1YSEiWrt2Lc2ePdsg2xZSXIiIqlSpIqppxejatavoCEbRpEmTT/774cOHScCJM6O3wyIVKlQwu4O88ePH06hRo3ho/v+oVCpavXq1YbYtYliM6O1OmfsXy6lTp6hixYqp16KykpShz3v37lHevHk/e4Q4Y8YMGjNmjJHTsRQVKlSgc+fOiY5hFGvXrqU8efJQnTp1REdRlMTERHr9+jU5OzvLul1hZy4rV66kyMhIUc0rQpUqVahu3bqiYxjEuHHj6M6dO1S9evUvDj3MmzfPiKnYh7Zt20Zr164VHcNgJEmiFy9e0K+//kqWlpZcWD7BwsLCIJMatLJvkYiePXv21de0bt2aunfvTjt37jREBOHS0gdEWXd4cOzYsTRx4kTau3fvF/vi33//NWIq85KW96C1tTUdP36cunfvboRExjdgwACytbUlHx8fKlSo0Bf7xNXV1YjJjCOt30Pffvut7G0bZFgsOjo6Ta8DkCX/Q4nS3gdERC4uLgZMIoa5778S8P8BUVRUVJpvFMyKfSDyPWCUay4bNmygLl260IMHD8jLy8vQzSlSzZo1ydnZmXbs2CE6ihAXL16ksmXL0q5du8x6dQaRqlSpQjlz5qTNmzeLjiLE2bNnqVKlSrRv3z5q0KCB6DhCfPfdd3T8+HG6du2awWfKGeWaS8uWLcnS0pICAwON0Zwi+fj40J49e+jly5eiowhRunRpKliwIAUEBIiOYpYePHhAp0+fJh8fH9FRhAkICCA3Nzezve6SlJREW7duJR8fH6NMwTZKcbG3t6emTZuSv7+/MZpTJG9vb0pMTDTbMxeVSkW+vr60ZcsWSkpKEh3H7AQGBpKlpSW1bNlSdBQhAJC/vz+1a9eOtFqDXGpWvAMHDtDz58+Ndn+Z0WaL+fj40IkTJ+jRo0fGalJRcufOTVWrVjXrAuvj40PR0dF08OBB0VHMjr+/PzVp0oQcHBxERxHiv//+o7t375r1mZu/vz8VLFiQSpcubZT2jFZcWrVqRRYWFmY73kv09o70f/75h2JiYkRHEaJcuXKUP39+HhozskePHtHJkyfNekWEgIAAcnFxoXr16omOIkRSUhJt2bKFfH19jbYqgdGKi6OjIzVu3Nisj9y9vb0pISGBgoKCREcRQqVSkY+PD23ZsoWSk5NFxzEbgYGBZGFhQa1atRIdRYiUIbG2bdua7ZqGhw4doujoaKOeuRn1JkpfX186duwYPX782JjNKkaePHmocuXKZn3k7uvrS1FRUXT48GHRUcxGQEAANW7cmBwdHUVHESIkJIRu375t9mdu+fPnN+qzfIxaXFq3bk06nc6sh8Z8fHxo165dZvsskwoVKlDevHnN+gzWmB4/fkzHjh0z+2sNTk5OVL9+fdFRhEhOTqbNmzcbbZZYCqMWFycnJ2rUqJFZH7n7+PhQfHx8ll2Z4GtShsY2b95Mer1edJwsb/PmzaTT6ahNmzaiowjx7pCYuTzi4kNHjhyhqKgoo5+5GX1tMV9fXzp69CiFhYUZu2lFyJcvH1WsWNGsj9x9fX3p6dOndOTIEdFRsjx/f39q1KgROTk5iY4ixOXLl+nmzZtmPSTm7+9PefPmpQoVKhi1XaMXl9atW5NGo6EtW7YYu2nF8PHxoeDgYHr9+rXoKEJUqlSJvLy8zPoM1hjCwsLo33//NeshsYCAAHJ0dKSGDRuKjiKEXq8XMiRGJKC4uLi4UMOGDc36yN3Hx4fevHlDwcHBoqMIkTI0FhgYyENjBrR582bSaDRmOyRG9PaovU2bNmY7JHb06FGKjIwUcuYmZMl9Hx8fOnLkCEVERIhoXrgCBQpQuXLlzPrI3cfHhyIiIujYsWOio2RZAQEB1KBBgyy5IGNaXL16la5du2b2Z25eXl5UqVIlo7ctpLi0bduWVCqVWQ+N+fr6UlBQEMXFxYmOIkSVKlUoV65cZn0Ga0gRERF05MgRs7/WYG9vT40bNxYdRQi9Xk+BgYFChsSIBBUXV1dXql+/vll/sfj4+FBcXBzt2rVLdBQh1Go1eXt7U2BgIEmSJDpOlrN582ZSqVRmPyTWunVrsrS0FB1FiGPHjlF4eLiwMzdhT6L09fWlQ4cO0dOnT0VFEKpQoUJUpkwZsx4a8/X1pbCwMDp+/LjoKFlOQEAA1a9fn9zc3ERHEeLatWt05coVsz5zCwgIoFy5cgl7IKGw4sJDY2/PXnbs2EFv3rwRHUWIatWqkaenp1mfwRpCZGQkHTp0yOyvNdjZ2ZntkJgkSRQYGEje3t5pflia3IQVF3d3d6pbt67ZH7m/fv2a/vnnH9FRhOChMcPYunUrqVQqateunegowgQEBFCrVq3I2tpadBQhTpw4QU+ePBF65iasuBC9/XI9cOAARUVFiYwhTJEiRahUqVJmfeTu6+tLjx8/ppMnT4qOkmX4+/tT3bp1yd3dXXQUIW7evEkhISFmPSTm7+9Pnp6eVK1aNWEZhBaXdu3aEQDatm2byBhCpQyNxcfHi44iRPXq1Sl79uxmfQYrp6ioKDp48KDZD4nZ2tqa7eO0lTAkRiS4uGTLlo3q1Klj9kfur169oj179oiOIoRGoyFvb28KCAjgoTEZbN26lQCY9ZCYv78/tWzZ0myHxE6dOkWhoaHCz9yEFheit0fu+/fvp+joaNFRhChWrBgVL17crI/cfXx86NGjR3TmzBnRUUxeQEAA1a5dmzw8PERHEeL27dt04cIFsz9zy549O1WvXl1oDuHFpX379qTX6816aMzX15e2bdtGCQkJoqMIUatWLcqWLZtZn8HKITo6mvbv3y/8iFWkgIAAsrGxoebNm4uOIgQACggIIG9vb9JoNEKzCC8u2bNnp1q1apn1F4uPjw/FxMTQ3r17RUcRQqPRUPv27SkgIIAAiI5jsrZu3Up6vZ7at28vOoow/v7+1Lx5c7KxsREdRYjTp0/Tw4cPFXHmJry4EL09ct+3bx89f/5cdBQhSpQoQUWLFjXroTFfX1968OABnT17VnQUkxUQEEC1atWi7Nmzi44ixN27d+n8+fNmf+aWLVs2qlWrlugoyigu7du3p+TkZNq+fbvoKEKkrBK8bds2SkxMFB1HiNq1a5Obm5tZn8FmxvPnz2nfvn2KOGIVJSAggKysrMx6SMzf35/at28vfEiMSCHFxdPTk2rUqGH2R+4vXryg/fv3i44ihFar5aGxTNi+fTslJSWRt7e36CjCBAQEUPPmzcnOzk50FCHOnTtHDx48UMyZmyKKC9Hb6w579uyhly9fio4iRKlSpahQoUJmfeTu4+ND9+7do/Pnz4uOYnL8/f2pRo0a5OnpKTqKEPfv36czZ86Y9Zmbv78/ubm5Ue3atUVHISIFFRdvb29KTEykHTt2iI4ihEqlIl9fX9q6dSslJSWJjiNEvXr1yNXV1azPYDPi5cuXtGfPHsUcsYoQGBhIlpaW1LJlS9FRhEiZJda+fXvSarWi4xCRgopLrly5qHr16mZ95O7r60vPnz+nAwcOiI4ihFarpXbt2pG/vz8PjaUDD4m9PWpv1qwZ2dvbi44ixH///Ud3795V1AGGYooL0dthkX/++YdiYmJERxGiTJkyVKBAAbM+cvfx8aE7d+7QxYsXRUcxGQEBAVStWjXKlSuX6ChCPHz4kE6dOmXWQ2IBAQHk6upKdevWFR0llaKKi7e3NyUkJFBQUJDoKEKkDI1t2bLFbIfG6tevT87OzmZ9BpseMTEx9M8//yjqiNXYAgMDycLCglq1aiU6ihAps8TatWunmCExIoUVFy8vL6pSpYrZH7k/e/aMDh8+LDqKEDqdjtq2bctDY2kUFBRECQkJZj0kFhAQQE2aNCEHBwfRUYQICQmh27dvK+7MTVHFhejtdYddu3ZRbGys6ChClC9fnvLly2fWR+6+vr5069YtunTpkugoiufv709VqlQhLy8v0VGECA0NpePHj5v1mZu/vz85OztT/fr1RUd5j+KKi7e3N8XHx5v10JiPjw9t3ryZkpOTRccRokGDBuTk5GTWBTYtXr16Rbt27VLcEasxBQYGkk6nM/shsbZt25JOpxMd5z2KKy558+alSpUqmfXQmK+vL0VFRdGRI0dERxHCwsKC2rRpw0NjX7Fz505KSEgw6+ISEBBAjRs3JicnJ9FRhLh8+TLdvHlTkWduiisuRG+vOwQHB9Pr169FRxGiYsWKlCdPHrM+cvfx8aEbN27QlStXREdRLH9/f6pYsSLlzZtXdBQhnjx5QseOHTPr4urv709OTk7UoEED0VE+osji4uvrS2/evKHg4GDRUYR4d2hMr9eLjiNEo0aNyMHBwazPYL8kNjaWgoODFXnEaiybN28mrVZLbdq0ER1FmICAAGrTpg1ZWFiIjvIRRRaXfPnyUYUKFcz6yN3X15ciIyPp6NGjoqMIYWlpmTo0xj4WHBxM8fHxZn/U3rBhQ3J2dhYdRYgrV67QtWvXFHuAocjiQvR2WGTnzp0UFxcnOooQlStXpty5c5v1kbuPjw9dvXqVrl69KjqK4gQEBFD58uUpf/78oqMIER4eTkePHjXr4hoQEEAODg7UsGFD0VE+SdHFJS4ujnbt2iU6ihApQ2OBgYFmOzTWuHFjsre3N+sC+ylxcXG0c+dOxR6xGsPmzZtJo9FQ27ZtRUcRxt/fn9q0aUOWlpaio3ySYotLwYIFqWzZsmb9xeLj40Ph4eF0/Phx0VGEsLKyolatWpn1e+BTdu3aRXFxcWZ/1F6/fn1ycXERHUWIa9eu0ZUrVxT9HlBscSF6e91hx44d9ObNG9FRhKhatSrlzJnTrK87+Pr60qVLl+jGjRuioyiGv78/lS1blgoWLCg6ihCRkZF0+PBhsz5zCwgIIHt7e2rcuLHoKJ+l6OJSrFgxev36NWXLlo0sLCzI1dWVevXqZTbP+1Cr1VSrVi1asWIFubi4mGUfZMuWjbRaLZUrV84s95+I6Pz589SrVy9ydXUlnU5HGzduJLVabbZ9kCNHDpIkiQ4ePGg2ffDu/ltYWNCUKVPI3d1d2dcjoUBJSUnw8/MDEX30R6vVgojg5+eHpKQk0VENxtz74N39V6lUZrf/wPt9kLLPKX80Go3Z94E5vA++tP9qtVrR+6/I4uLn5/fRF8qHf1QqFfz8/ERHNRhz7wNz33+A+wDgPjDl/VdccTl37twXO/LDP+fOnRMdWXbm3gfmvv8A9wHAfWDq+6+4ay4LFixI8zMJtFotLVy40MCJjM/c+8Dc95+I+4CI+8DU918FKGtlQFdXV4qOjk7z611cXOjZs2cGTGR85t4H5r7/RNwHRNwHpr7/iisuFhYW6XoKo06no8TERAMmMj5z7wNz338i7gMi7gNT33/FDYvZ29sb9PWmwNz7wNz3n4j7gIj7wNT3X3HFpW3btukaZ2zXrp2BExmfufeBue8/EfcBEfeBye+/2PkEHzP1GRJyMPc+MPf9B7gPAO4DU99/xRUXwLTndsvF3PvA3Pcf4D4AuA9Mef8VWVzM/a5cgPvA3Pcf4D4AuA9Mef8VWVxSnDt3Dr169YKDgwOICA4ODujVq5fiTv8Mydz7wNz3H+A+ALgPTHH/FV1cUqSMPSq5Iw3N3PvA3Pcf4D4AuA9Maf8VN1uMMcaY6ePiwhhjTHZcXBhjjMmOiwtjjDHZcXFhjDEmOy4ujDHGZMfFhTHGmOy4uDDGGJMdFxfGGGOy4+LCGGNMdlxcGGOMyY6LC2OMMdlxcWGMMSY7Li6MMcZkx8WFMcaY7Li4MMYYkx0XF8YYY7Lj4sIYY0x2XFwYY4zJTis6wJfo9Xp6+PAhHTlyhIiIgoODKSEhgYoXL06Ojo6C0xmHufeBue8/EfdByv5fuXKFTp8+TUREISEhVKBAAbPYfyLTfA+oAEB0iA8BoJCQEJo5cybt27ePAJCjoyMBoJiYGPLw8KBevXpRz549ycHBQXRcgzD3PjD3/SfiPvhw/4mInJycKCkpiWJiYihHjhxZev+JTPw9AIXR6/XYsGEDPD09UbVqVaxbtw43b97E48eP8ejRI4SEhOCXX35BgQIF0LJlS4SGhoqOLDtz7wNz33+A+8Dc9x8w/T5QXHHZuXMn3Nzc0K9fP0RFRUGSJKxduxbFihVD2bJlcfnyZUiShGvXrqFWrVpo3rw5Xrx4ITq2rMy9D8x9/wHuA3Pff8D0+0BRxSUyMhKlSpWCt7c3YmJiIEkSAGDu3LkgIlhZWeHs2bMAAEmScPPmTRQtWhQzZ84UGVtW5t4H5r7/APeBue8/kDX6QFGzxbZu3UphYWE0ceJEsrOzI5VK9dnXqlQqKliwIA0bNoxWrFhBz549M2JSwzH3PjD3/SfiPjD3/SfKGn2gmOKi1+tp586dVLlyZfLy8qLw8HAKCwujsLAwiomJIaK3F7eioqJS/z0iIoKaNm1K8fHxdOHCBbE7IANz7wNz338i7gNz33+irNMHipmKHB8fT3fu3KFWrVrR8uXLafbs2ak/i4uLIyKihIQE6tq1K2m1b2O7uLhQUFAQ5cqVi27evEkNGjQQkl0u5t4H5r7/RNwH5r7/RFmnDxRTXPR6PSUkJJCdnR3FxsZSRETEJ1/37ilfcnIyERFZW1undropM/c+MPf9J+I+MPf9J8o6faCY4mJpaUnOzs4UGhpKzZo1o759+6b+7NKlS3Ts2DHSaDTUrl07cnNzIyIiOzs70ul0FBUVRR4eHqKiy8bc+8Dc95+I+8Dc958oC/WByNkEH+rXrx/KlSuHly9fQpKk1D8fzpB492fnz5+Hp6cnLl68KDq+LMy9D8x9/wHuA3PffyBr9IFiLugTEXXo0IHu3r1LO3bsIKK3syA+NUsi5d+Tk5Np2bJlVKpUKSpSpIix4xqEOffB2bNn6cGDB3T58mWz3P8UGXkPLFmyhJycnMjT09PYcWVnzp+BFFmhDxRVXKpXr06tW7emSZMm0cWLFwlfWJlGr9fThg0byN/fn0aPHk2WlpZGTGpYkiTRxIkT09QHGzdupK1bt5psH8TGxtLSpUupQoUKVKlSJQoJCaHixYun+T1g6vv/Ken9HGzcuJE2bNhA165do3z58lGfPn3o/PnzRkwsr4x8D2zYsIGGDBmSZd4DhQoVIicnJ9P+HhB52vQpoaGhqFmzJgoXLozt27fjzZs3CA4ORseOHdGtWzfcuXMH0dHRmDVrFpydnUFE6NixI6KiokRHz5S4uDiMGDECKpUK5cuXR4UKFdLUBzly5MDcuXOh1+tF70K6/Pfff+jbty/s7e2hVqvRsmVL7NixA8nJyel6D5jq/n9NRvrg/v37mDRpEnLmzAkiQqVKlbB8+XLExsaK3p10S8/+u7m5QaPRoFChQjhx4oTo6JkWGBgId3d3ODk5oWjRoib7OVBccQGAR48eoV27drC2tkbDhg3x66+/wt/fH+vXr8f48eNRtmxZ5M+fHytXrsS6devg7OwMDw8PbN26VXT0DDl58iSKFi0KCwsLzJgxA8nJyXj06BE6d+4MZ2dnNGrU6LN9sGrVKiQlJYnehTR5/fo1Vq5cicqVK4OI4OnpiYkTJ+LBgwcfvfbRo0fo2LHjV98DprT/6fW190CZMmU+2QdJSUnYunUrmjVrBpVKBQcHB/Tv318xY/FplbL/tra2aNCgwRffAyEhIahUqRLUajXGjBmDN2/eiI6fblFRUejSpQuICG3btkV4eHiG3wNKoMjiAgBDhw6FtbU1OnXqhJIlSyJ37tzIly8fateujWnTpuHu3bupr33y5AlatWoFIkK3bt0QHR0tMHnaxcfHY+zYsVCr1ahYsSKuXLny0c93796NHj16vNcH1tbWKFKkyHt9oGSXLl3CwIED4ejoCJVKhSZNmmDLli1f/TAsXboURIRWrVp99T2QVX3uPeDq6goXFxfcvHnzi79/7949TJgwAdmzZwcRoVq1alizZg3i4uKMtAeZc/ToURARateu/dX3QFJSEqZPnw4LCwsUL14cZ86cEZg8fbZv347s2bPD2dkZf/75Z+pyL8Dn3wNeXl7Q6XQ4ffq0wOSfp8jiEhERARsbG0yYMAGSJCE2NhZPnz5FdHQ0EhISPvk7kiRhzZo1cHR0hKenJ3bu3Gnk1Olz9uxZlChRAjqdDtOmTfviF+2HfbBmzRoQkaI/PG/evMG6detQo0YNEBGyZcuGcePGpbkgJCUloUCBAmjbtm2a3wNZ2Yd9cOrUKRAR1qxZk6bfT0xMREBAABo1agQigrOzM4YMGYKrV68aOHnmtGjRAkWLFkVSUlKa3wOXLl1C+fLlodFo8P333yv6/fL8+XP06NEDRIQWLVrg8ePHn33th++BJ0+ewM7ODqNHjzZi4rRTZHEZPXo07OzsMnQd5dGjR2jatCmICN99952iVgkFgISEBEycOBEajQZly5bN0FBFcnIyChcujFatWhkgYeZcv34dw4YNg4uLC4gIDRo0wKZNm9L9AU8poOfPnzdQUtPXunVrFCpUKN3DIbdu3cLo0aPh7u6eelbw119/IT4+3kBJM+bMmTMgIvz111/p/t3ExERMmTIFWq0WpUuXVuT7KDg4GDlz5oSDgwNWrVr13tlKWo0bNw62trZ4+vSpARJmjuKKy9OnT2Fra4uxY8dmeBuSJGH58uWwt7dHrly58M8//8iYMOMuXLiAMmXKQKvVYvLkyUhMTMzwttauXQsiwrlz52RMmDHx8fHYsGED6tatCyKCq6srRo4c+dUhm89JSkpCoUKFFFk8leTs2bMgIqxbty5Dv//h/5ubm1um/t/k1qpVKxQuXBjJyckZ3sZ///2H0qVLy/KZk8vLly/Rq1cvEBGaNGmChw8fZnhbcnxfGoriiouclfjBgwdo2LAhiAh9+vRBTEyMDAnTLzExET/++CO0Wi1KlSolS0FISkpCwYIF0bZtWxkSZszt27c/eQSc2Yupf/75J4godUlx9nktWrRAkSJFMvUFDADXrl3DsGHDUmdgZvSMUy7nz58HEWHt2rWZ3ta7owXlypVDSEiIDAkzZu/evcidOzfs7OywdOnSDJ2tfCgzIz2GpKjiEhUVJfsYoiRJWLRoEWxtbZEnTx7s379ftm2nxaVLl1ChQgVoNBpMmDBB1qGH1atXg4hw4cIF2bb5NR+O3Ts5OWHIkCEfTUbIqOTkZBQpUgQtWrSQZXtZ3enTp0FEWL9+vSzbi4uLw9q1a1OvlXl4eKTrWplc2rZti4IFC8o6A+rMmTMoXrx4mq5zyu3Vq1fo27cviAj169fH/fv3Zdt2ZGRk6jVqJVFUcZkwYQJsbGwQGRkp+7bv3r2bevo/YMAAvHr1SvY23vXuzJVixYoZZEZHykXv9u3by77tD92/f/+jWUerV6+WfdbR+vXrQUSKnQGjRM2aNUOxYsUyffbyoQ9n+TVt2jRNs/wy68KFCyAirF69WvZtvztDs1KlSrIdFH3JwYMHkTdvXtjY2GDBggUGuRdl5MiRsLe3x7Nnz2TfdkYpprg8e/YM9vb2GDlypMHa0Ov1mD9/PmxsbJA/f34cOXLEIO1cvXoVlStXhlqtxujRow06537lypUgIoPcw5CUlIRt27ahefPmRrlfIjk5GcWKFUOzZs0Msv2s6uTJkyAi/P333wbZfmxs7Ef3J/3www+ZulbwJe3bt0eBAgUMWsROnjyJIkWKwNLSEr/++qvshRl422+DBg1KHTK+c+eO7G2kCA8Ph7W1NSZOnGiwNtJLMcVl4sSJsLa2Rnh4uMHbunXrFmrUqAGVSoWhQ4fi9evXsmw3OTkZs2bNgqWlJQoXLozjx4/Lst0vSUxMRL58+eDj4yPbNh89eoTJkycjV65cICJUrFjRKHd6//333yCiLHGXtbE1adIEJUqUMPgd2ikrK9jZ2UGtVqNVq1YICgqS7cv54sWLICKsXLlSlu19yburYlSrVg3Xr1+XbdtHjx5FgQIFYG1tjd9//90od84PHz4cDg4OirnPTxHF5fnz53BwcMCwYcOM1mZycjLmzJkDKysrFCpUCMeOHcvU9m7evInq1atDpVJh+PDhRr1JbdmyZSAiXLp0KcPbSE5ORnBwMNq0aQO1Wg1bW1v4+fkZbTaaXq9HiRIl0LhxY6O0l9UcO3YMRAR/f3+jtBcTE4MlS5agXLlyICJ4eXlh6tSpX7xPIy18fX2RL18+o87q+vfff1GwYEFYWVlhzpw5mSoEcXFxGDZsGFQqFapXr27UmXdhYWGwsrLC5MmTjdbmlyiiuEyePBlWVlYICwszetvXr19H1apVoVarMWrUqHQPYen1esydOxfW1tYoUKCAwYbaviQhIQF58uRBx44d0/27YWFhmDZtGvLkyQMiQpkyZbBo0SK8fPnSAEk/z9/fH0SU6SJvzho2bIhSpUoZdX0pSZJw+vRp9OrVCzY2NtBoNGjXrh3++eefdOe4fPkyVCoVli1bZqC0n/f69WsMHjwYRIRatWrh1q1b6d7GiRMnULhwYVhaWmLWrFkGGWr7miFDhsDJyUkR9/cJLy4vXrxInXEkSnJyMmbMmAELCwsULVoUp06dStPv3blzB7Vr1wYRYdCgQUIXCFyyZAlUKlWaLlDq9Xrs2bMH3t7e0Gq1sLa2Rs+ePXHy5ElZpkaml16vR6lSpdCwYUOjt52VpCyVEhgYKKT9Fy9e4I8//kCpUqVARMifPz+mT5+e5qHujh07Ik+ePELvqD906BDy5csHGxsbzJ8/P00F8s2bNxg9ejTUajUqV66Ma9euGSHppz1+/BiWlpb48ccfhWVIIby4/Pjjj7C0tMz06bQcrly5gooVK0KtVmP8+PGfnTas1+uxYMEC2NraIm/evDh48KBxg35CQkICvLy80Llz58++JjIyEjNmzECBAgVARChRogTmzZuH58+fGy/oJwQGBoKIcPToUaE5soL69eujTJkyQlfHlSQJx44dQ/fu3WFlZQWdTocOHTpg//79nz14uXLlClQqFZYsWWLktB979eoV+vfvDyJCvXr1cO/evc++NmV6s4WFBaZPn66IxSMHDRoEZ2dno48+fEhocXn58iWcnZ0xaNAgkTHek5SUhJ9++gk6nQ4lS5b86JrD/fv30aBBAxAR+vbtK+zGzE9ZtGgRVCrVe0dOkiTh4MGD6NSpE3Q6HSwtLfHNN9/g6NGjQs5SPqTX61GmTBnUr19fdJQs4fDhwyAibNmyRXQUAG9ngf72228oWrQoiAiFCxfGrFmzPrpJunPnzsidO7ei1gHbu3cvvLy8YGdnh8WLF3+0mOSECROg0WhQvnz5TF3vlFtoaCgsLCzw008/Cc0htLj89NNPsLCwwKNHj0TG+KSLFy+ibNmy0Gg0+OGHHxAfH4+lS5fCzs4OuXPnxp49e0RH/Eh8fDxy5cqFrl274tmzZ5gzZw6KFCmS+qGePXu24u7i3bJlC4gIhw4dEh0ly6hTpw7KlSuniIOHFJIk4fDhw+jcuTMsLCxgYWGBrl274siRI7h69SpUKhUWLlwoOuZHXr58id69e4OI0KhRIzx8+BDnz59HqVKloNPpMHXqVEUsKfOh/v37w8XFRejBr7DiEhMTAxcXF/Tv319UhK9KTEzEpEmToNVqYW9vDyJCr169FHGx7FMkSUqdqaLT6aDT6dCxY0ccPHhQUV80KSRJQrly5VCnTh3RUbKUAwcOgIiwfft20VE+KTIyEjNnzkTBggVBRHB0dISjo6OQCT1ptXv3buTMmROWlpZQq9UoXbq0UVfGSK+HDx9Cp9Nh+vTpwjIIKy7Tp0+HTqcz2I1YcpAkCatWrYKtrS20Wi20Wq0ij1SeP3+O+fPno2TJkiCi1FP1iIgI0dG+aPv27SAiHDhwQHSULEWSJNSqVQsVKlRQ5EFFCr1en7qEkVqthpWVFXr06IETJ04oLndISAhKlSoFlUoFIkLTpk0RGhoqOtYX9e3bF66urgZfjeRzhBSXV69ewdXVFX379hXRfJo8fvwYLVq0ABGhe/fuCAsLSx1jrVChAi5fviw0nyRJOHXqFL777jtYW1tDo9HA29sbe/bswe+//w6NRpOh6ZTGIkkSKlSogFq1ainuiyQr2LdvH4gIQUFBoqN8Uffu3eHp6Yl79+7h559/Rt68eUFEKF26NBYuXCj8onRSUhKmTZsGnU6HEiVK4OzZs9ixYweyZ88OJycnrF27VrHv3wcPHkCn02HGjBlC2hdSXGbMmAGdTvfJx9uKJkkS1q1bBycnJ2TPnh3btm177+enT59GsWLFYGFhgV9++cXos0NiYmKwePFilC1bFkSEPHny4KeffsKTJ09SX/PmzRvkyJED3377rVGzpUdQUBCICPv27RMdJUuSJAk1atRApUqVFPvld+vWLWg0GsybNy/13/R6PXbt2oW2bdtCo9HA1tYW//vf/4SskP3u7NFx48a9N3v02bNn+Oabb0BEaN26tWKH9Pz8/ODu7i7kNgmjF5fY2Fi4u7vDz8/P2E1/VXh4ONq2bQsiQpcuXT578fvdee1VqlQxyrz28+fPw8/PL3XZjdatW2Pnzp2fvVFr7ty50Gg0uH37tsGzpZckSahUqRJq1Kih2C++rGDPnj0gIgQHB4uO8knffvstcuTI8dkbl0NDQzFlypTUZYgqVKiApUuXGnyYJzk5Gb/++issLS2/et/b5s2bkS1bNri4uGD9+vWKez/fu3cPWq0WM2fONHrbRi8uM2fOhFar/eLccRH+/vtvuLq6wt3dPc03oR0/ftygd+TGxsZi+fLlqFSpEogIOXPmxKRJk9J0nSouLg4eHh747rvvZM0kh+DgYBCRYh7illVJkoSqVauiSpUqivvSu337NjQaDX777bevvjYpKQnbt29HixYtoFKpYG9vj379+hnkgnrKih0qlQojR45M0zJOT58+RceOHUFE8Pb2Vty1zl69eiFbtmyyraGYVkYtLq9fv0a2bNnQq1cvYzb7RZGRkfD19QURwcfHJ93L/b+7llCNGjVkWUsoJCQEAwYMgIODA1QqFZo1a4atW7emewhu9uzZ0Gq1Rn8Wx5dIkoQqVaqgatWqivvCy4p27dqlyELeq1cveHh4pHsNvvv37+P7779Hjhw5QESoWrUqVq1alekvTjnWGty0aRNcXV3h5uZmtDXe0uLOnTvQaDSYM2eOUds1anGZM2cONBqNQZeeTo/AwEC4u7vD1dUVGzduzNS2jhw5kqlVUOPi4rBmzRpUr1499SFN48ePz9QZXkox7927d4a3Ibd//vkHRIRdu3aJjmIWJElC5cqVUb16dcUU85ShmtmzZ2d4G4mJidi8eTMaN26c+tC6wYMHZ+j5LLdu3ULNmjVlWSU9PDwc7dq1AxGhY8eOirmvrGfPnsiePbtRF9Q1WnGJi4tD9uzZ0bNnT2M1+VlRUVHo3LkziAht27aVbZn/2NhYDBw4EESEOnXqpKmIXrt2DUOHDk19vGzDhg0REBAg23TnlGFIOZ98l1GSJKF69eqoXLmyYr7ozMHOnTtBRNi7d6/oKACA3r17yzpMc+fOHYwdOxbZsmVLXXjyzz///OoitB8+3+nw4cOy5JEkCevXr4ezszM8PDywdetWWbabGSnDkHPnzjVam0YrLkq5wLxt27bUaYR//vmnQb7kDhw4gLx588LW1hYLFy786CwmPj4e69evT1300t3dHaNHjzbI1OGUCRR9+vSRfdvptXfvXhARdu7cKTqKWZEkCRUrVkTNmjWFF/X79+8b7AJzQkICNm7ciPr164OI4OrqiuHDh+PGjRsfvfbevXuoV68eiAj9+/c3yCSBJ0+eoGXLliAidOvWTfhzVnr06PHFCRRyM0pxSZka26NHD2M090nR0dHo3r07iAgtWrQw+EKZMTExqc/MbtCgAe7fv4+bN29i5MiRcHNzAxGhbt262LBhw2cXyJSLEqZ+S5KEmjVromLFisK/4MzRjh07QETYv3+/0Bx9+vSBm5ubwafG3rhxAyNGjICrq2vqApQbN25EfHw8Fi9eDDs7O3h5eRl8KrwkSVizZg0cHR2RI0cOofcd3bx5E2q1+r2p34ZklOIyf/58qNVqoz44513BwcHw9PSEg4MDVq1aZdQvt+DgYLi6ukKj0aSODQ8bNsyoy3Kn3LQqcqkdpS9JktVJkoTy5csLXWonZUmSX375xWhtvnnzBn/++Sdq1aoFIoKFhQWICJ06dfp/7Z13XFTH9/fPLktHUOwUUUFAmgoGUb927AWxoLHEjg1jSTTRWFBi+WmiMRErKraYRGNPLLHG3kUlGjX2hgUEG7C79/P84bNE4sLuvXvvLrvM+/XKH9k7Z+bI3N0zM+fMOUa9oHnv3j20atUKRIR+/fqZLIVUr1694ObmZpTdi+TGJTs7G+7u7ujVq5fUQ33AixcvMGDAABARWrZsadRUMzdv3sT48eNRvnx5EFHeeXBkZKRJEnXOmDHDpElCGzVqhNDQULZrMSFbtmwxaZLQYcOGmSQdCcdxWL58ORwdHeHk5AQnJycQEVq0aIFff/3VaOmcOI5DUlISSpQoAQ8PD5NE8F29ehVyuRyJiYmSjyW5cUlMTIRcLhe1PrU+7NmzB56ennBycsLSpUuN8qOmVCqxefNmtGrVCjKZDC4uLoiLi8tLx63ZQbm4uCA5OdmoP7SaRKFxcXFGG1PDwYMHQURFwrFZnOE4DjVr1kSTJk2MPva9e/dgY2ODGTNmGHXc+/fvo3Xr1nk7hoyMDLx+/RorV65EREQEiAgVK1bExIkTjXZsfOfOHURGRoKIEBsba/TMxT169ICHh4fkx/GSGhdNCvgePXpIOUw+srKyMHjwYBARmjZtapQoqbt372Ly5Mlwd3cHESE8PBzLly/Xeq78vu+nXbt2+dK2SM3XX39tksJsTZo0Qc2aNdmupQiwadMmEJHRy3HHxcUZNQW8vr6OCxcuYOjQoShRogTkcjnatm2Lbdu2SV6imOM4LFq0CI6OjvDy8jKqL0xT4mDRokWSjiOpcdEUr/rrr7+kHCYPTZSWg4MDEhMTJa3Gp1KpsGPHDrRv3x5yuRxOTk4YMmQIzp8/r5f81q1bUb58eZQqVUqyqLX/kpmZmXcfwFj8+eefICJs2rTJaGMyCkatViMkJATNmjUz2pia0rvGKl716NEjdOjQAUSEXr166RWl9fLlSyxbtgy1a9cGEcHT0xNTp06VPPPxzZs30bhxYxARhg8fbrQjw+7du6NSpUqSFmeTzLhoyu5269ZNqiHyeP9+ScOGDSW9pPnw4UMkJCSgUqVKICLUqlULS5YsEbQie/bsGXr06AEiQnR0tGj3bQpj6tSpsLOzM9qOqVmzZggODjZp2V1GfjZs2AAiwpEjR4wy3qeffoqSJUtK7sTW3C9xdXVFuXLlBFfjPHPmDAYNGgRHR0dYWVmhY8eO2Llzp2TvsFT3bQrj8uXLkpeVlsy4LF26FDKZTPLU9IbejNcHtVqN3bt3o1OnTrCysoKDgwMGDBiAU6dOibLj2Lhxo2iZAnSRkZEBFxcXjB49WtJxAODIkSMgoiKVCoPx7n0OCgpCixYtJB/r4cOHsLOzw9SpUyUdJy0tDZ06dcqLBPtvGWUhZGZmYuHChahRowaICJUrV8aMGTMkWwRev34d9evXh0wmw8iRIyXPBda1a1d4eXlJFtAgiXHJzc1F5cqV0bVrVym6B5A/p1e9evUkCXNOS0vDrFmzULVqVRARgoODsWDBAklWYE+ePEGXLl1AROjatasoX46CmDJlCuzt7SXfKbVo0QJBQUFs11IE+fnnn0FEOH78uKTjjB49Gi4uLsjIyJBsjA0bNqBMmTKS5fTiOA7Hjx9H3759YW9vD4VCga5du2Lv3r2iv9ti5DjTl4sXL4KIkJSUJEn/khiXpKQkEBEuXrwoRfc4fvy4ZNmIOY7D/v370a1bN1hbW8POzg6ffPIJjh49ahS/yE8//ZS3rZfKT5Geng5nZ2d89tlnkvQPvJsjIpJ8J8YQhlqtRkBAAFq1aiXZGI8fP4a9vT2mTJkiSf/Pnj3Ly0bcqVMno2QjTk9Px/z58xEQEAAigo+PD+bMmSP6YvC/2ZmlupfSuXNnVKlSRZLdi+jGJTc3F1WqVEHnzp3F7jpfHZXw8HBRLyI+e/YM3377LXx9fUFE8Pf3x7x58/D8+XPRxtCXR48eISoqCkSEnj17SqLDpEmTYG9vL9kXslWrVggICGC7liLM+vXrQUSF1isxhM8++wzOzs6SpD3ZsmULypcvD1dXV6xfv97okYgcx+Hw4cPo2bMnbG1tYWNjg48//hiHDh0STReVSoX/+7//g42Njc66MkJJSUkBEWHFihWi9y26cVmxYgWISPRaC+9XgJw5c6YoFSA5jsOff/4p6QtiiG5r167Nq4i5fft2Uft//vw5SpQogbFjx4raLwCcPHkSRIT169eL3jdDPFQqFfz9/dGmTRvR+05LS4O9vT0mTZokar/p6elFrgLkfxem1atXF3VhWlhFTDGIjo6Gt7e36FV1RTUuSqUS3t7e6Nixo2h9Zmdn59WuDw0NzbuQaAjatrazZ8/mXcvFGDx48ABt2rQBEaFPnz6inl1PmDABDg4Oov+727RpA39/f8nvCjAMZ+3atSAinDp1StR+x44dixIlSoi6696xYwcqVqwIFxeXIlm7XnOkHhMTI/qRulKpxNdffw1ra2sEBQWJWvb53LlzICIkJyeL1icgsnFZtWoViAjnzp0Tpb9z584hODgY1tbWSEhIMOhc0JhOObHhOA4rV66Es7Mz3N3dRauF8uzZMzg5OeHLL78UpT8AOH36NIgIa9euFa1PhnSoVCr4+vqiffv2ovX55MkTODg4YMKECaL09+LFC/Tr1w9EhNatW0t+90QMpAoGSklJQc2aNWFlZYXJkyeLdk+lQ4cOqFatmqi7F9GMi1KpRLVq1dChQweD+8rNzUV8fDwUCgVq1Khh0BFbQeGERWE7zZe7d+/mFUcaOHCgKIn3vvzySzg5OYlW1Kh9+/bw9fVluxYzYvXq1SAinD17VpT+xHyndu3aBQ8PD5QoUQLLly8vcrsVXUhxjSE3NxdTpkwR5fdRw5kzZ0BEWLNmjcF9aRDNuKxZswZEZPB2TSzLbOyLUMaC4zgsXboUTk5O8PT0NLgA1NOnT+Ho6CjKKvPs2bMgIqxevdrgvhjGQ6lUwsfHB1FRUQb3JdZuOCsrC4MGDQIRoXnz5iYtFyEWDx48EO0CNvDu+xYcHAyFQoFp06YZHPHVrl07+Pn5ibYwFMW4qFQq+Pn5oV27doL7eP9MMTAwUJCR0qRwCAsLAxHBw8PDKCkcTMHt27fziiINHTrUoLQR48aNE+V8PCoqCj4+PqI7BhnSk5ycDCLSO31RQUyYMAGOjo4Ghebu3bsXXl5ecHR0xOLFi81ut6ILQ1NHvc/7PumwsDCDfNKaI+1169YJ7uN9RDEu69atM8gpaGg0xPXr1zFs2DCUKFECMpksL/mcpf/IqdVqJCYmwsHBAZUrV8aBAwcE9ZOWlgYHBwdMnDhRsC7nz5+XxCnIMA5KpRJVq1ZFdHS04D40EYjjxo0TJP/y5UsMGzYsr7jXzZs3BetiLmiS3rq5ueVLesvXoIoVTStmMI4MAIgnM2bMoJycHHr16hXVrVuXOnToUGBbGxsbrfK5ubmUnp5OEyZMIFdXV97yz549o9q1a1PDhg2pbNmyJJPJ9Ja3BKZMmULNmjWjiIgInW21/Q2mT59O6enpFBsbS1WqVOEtn5ubS0RE8fHx5OjoSFlZWWRvb08ODg40atQonfIM0zN16lRSKpXUuHFjCgwMpNKlSxfYtrB3QBfNmzenQ4cOCZJ/8+YN9evXjzZv3qzXWOZGQkICqVQqGj16NDk4OBTatqDfQo7j6PHjxzRmzBjy8PDgJT99+nR68eIFdevWjQICAkihUPCSLwxBxoWICACp1Wo6ePAg7dixg7777jve8tnZ2TRy5EiKi4uj4ODgAg2ENpRKJV26dIkOHjxIT548oZiYGAoNDeX5rzBfAND48eNp2LBhVKlSJUF9vH79mhITE8nW1pbi4uLIysqKtw5JSUk0aNAg4jiOZDIZ9erVi9atWydIH4bxyczMpNOnT9P58+cpKyuLpk2bxut7qItbt27R3bt3qVGjRrxlOY6jXr160dKlS8nJyUk0nYoa9+7do++//548PDyoQ4cOOhd72lAqlTR27Fjq3r071alTh9ccvnr1irZv304pKSkUEBBAvXv3FucdMHjvA+DKlSuYN2+eIFlNXYMvvvhC8HlhdnY2kpKS8M033wiSN1c4jsOAAQNw4cIFg86lU1NTERsbixs3bvCS05b8kuM4SdN4M6Tjzp07GDJkiGj9cRyHOnXqCJZv0qRJsYk65DgODx8+xNy5cwXXWeE4DsnJyfj8889x69YtQfJHjhwRLS2UaNFiSUlJvH+c3kfjmDIkDvzQoUNYtWqVYHlzhOM4JCYmYtKkSdi5cycePHggyNAolUpMmTKFV/RZcHCw1s9r1arFe3xG0eD3338XLSx94MCBgiOYOI4TNSzWnNi1a5dBVVuzs7PRp08fwQvOM2fOiHJPTdRLlJ07dzYoaonjOPj6+hqkQ3x8vOTlO4sir169wrFjx7BgwQLExcVprYKpC47jMGfOHL3q4aSmpha4Q5HJZLzHZhQdKlasaHAfe/bswcGDBwXLjxw50mAdzJlRo0YZtGvjOM6g0PLp06cbvMgQ1bhwHIf27dsbFKV1//59gytXBgUFGSRv7rx9+xYRERGC5Zs0aaJz1VPYMajYedAYxuX8+fMG/bC9evUKo0aNMkiHhg0bGiRv7nAch3r16hnUx7x58ww6Lo+IiDBIXpKsyJGRkQb14eXlZZD88ePHi+Xu5X0yMzNx+PBhQbIqlQqffPKJQeOb+2XV4s7//vc/wbJhYWG8f5Teb79x48Zi42spjKNHjxp8R693796CZd++fWtQUUG54SEB+bG2tqZ169bRmjVrBPeRkpJC+/fvFywfERFRrCLHtOHs7FxoiHhhWFlZUdeuXenu3buCx4+KihIsyzA9jRo1IugIJNX2fMmSJfTHH3/wijZatGgRxcfHU3JyMm3atImOHTvGO3LREqlXrx61adNG5zwUhq+vr94h4//Fzs6O6tSpQ/fv3xc2uGCzpINevXoZtKVq2LChQfLJyckWd7OXLw8fPjQocissLEywrJOTk2BZhunhOA5Dhgwp9Ds0ZcqUfDvUFy9eYPLkybzG2bdvH/bt24ecnBxcv34dKSkpxf57+z6vX7826IiR4zjUrVvXIB0++ugjQXKSGRfNyykUtVqNr776yiAdunfvbpC8JRASEiJYNjs7GwkJCYJkb9++jbS0NFFTgzOMy7Zt25CQkFCgDzQjIwNdunTB27dv8eLFC7Rq1YqXYVAqlZKWQrcU9u3bhx07dgiWf/jwIRITEwXLZ2dnY9q0abzlCr6OWQjPnz/Xq11BNzr1lc/MzDRIvly5cnq1M0f0/Rs0b97cIPnHjx8LkndycqIRI0ZQxYoVKSwsTK+xGMZF1xzWq1ePAgMDac6cObRo0aIPnqvVapo1axYNGTKEbG1tKTk5mdLT07X2pe32/6BBg2jhwoV6vYuFZQ8wZ/T5t9eoUYPGjx9Pbdu2FSRvY2NDqampgscnInry5Ile7d5H0A39gl4gbWhL7WJqeUvA1H9DNgfmj1jvAACdPhZt8s+ePSO5XD+3r6W+Q6b+Hkr6PRa8V3qPmJgYlC9fHnfv3hUkP2nSJIPqP/zyyy8goiJZSdIYcByH8PBw+Pv7C76E2rt3b3h5eQn20cyePRuOjo7svNyMmT17NpycnATP4ZIlSyCTyXD9+nXB8kQkWjE8c2TYsGEIDAwULD9+/Hg4OjoK/h0YP348ZDIZLl++LFgHDaIYl7S0NFSqVAm1atUSdHlPU7lOqI/l8uXLICIcOnRIkLwlcPXqVbi4uKB169aCwjgvX74MmUyGZcuWCRp/x44dICKLqLtRXOnbt69g521OTg68vLzQrVs3QfIHDx6EQqHAsGHDBMlbCo0bNxbsh9LU0vniiy8EyWuy28+ePVuQ/H8RzaF/4cIFODo6okuXLoLuOGhqbqenp/OWzcnJgUKhEJyTx1LYvXs35HK54NxAXbt2RZUqVQSl7Lh161axX3WaO+Hh4ejbt68g2aSkJMEr3n/++QelS5dGkyZNDC54Ze6UK1cO8fHxgmQnTpwIBwcHQSc4J0+ehK2tLXr37i3a6YOo0WKbNm0CEQn646SlpcHe3p53KKOG6tWrIy4uTpCsJfHdd98Jrqty8eJFEBFWrFjBW1atVsPBwaHYJQ+1FDiOg5OTk6BVa25uLqpUqSJoxZ2VlYWgoCB4e3uLltPMXHn69CmICL/88gtv2fT0dDg7O2Ps2LG8Ze/fv4+KFSsiIiICb9++5S1fEKKHIickJICIsGHDBt6yY8aMgYuLCzIyMnjLdu7cGU2bNuUtZ2loMiXb2Njg6NGjvOU7deoEb29vQSl8wsLC0L9/f95yDNNz584dEJGgkNcVK1aAiHDx4kVeciqVCu3bt0eJEiWQmprKe1xL49ChQyAiQbu/yZMnw97eHo8fP+Yl9+bNG9SuXRseHh549OgR73ELQ3TjwnEcunXrBnt7e5w7d46X7KNHj2BnZydo5zNp0iRUqFCBt5wlkpOTg//9738oV64cbx/IhQsXBO98evfubVBOM4bp2LlzJ4iId/VHpVIJb29vdOrUifeYX375JWQyGX777TfespbIokWLoFAoeAfVZGRkwMXFBWPGjOElx3EcunfvDnt7e5w9e5aXrD5Icony9evXCAsLg6enJ29LOmrUKJQsWZJ3tMNPP/0EIjK4DrylkJaWBi8vL9SsWZN3kEXHjh3h4+PDe/cya9YsODs7s4gxM+Tbb7+Fg4MDb39pcnIyiAgXLlzgJbd27VoQEebMmcNLzpIZMWIEqlevzlsuPj4ednZ2vHce06dPF3wMpw+S3dC/f/8+KlSogLp16/JKIvnw4UPY2dnxvhGq8RcITdZoiaSkpMDR0RGdO3fm9aNx7tw5EBFWr17Na7xt27aBiHDv3j2+qjJMTP/+/Xmn+1EqlfDx8UHHjh15yWmcx5988glbiLxH06ZN0blzZ14yL168QMmSJXmniNmyZQuISLCPWx8kMy4AcOLECdja2vIuXPPpp5+iVKlSyMzM1FsmOzsbcrkcS5YsEaKqxaIJspgyZQovuQ4dOsDX15dXWPONGzdARNi9ezdPLRmmJiIigncG3TVr1oCIeB1/S+U8tgQqVKiASZMm8ZJJSEiAra0tHj58qLeM0EUnXyQ1LsC/LyCfKKL79+/DxsYG06dP5zWWr69vsS8ypI2vv/6a9/b3zJkzICKsW7dObxmVSgU7OzvBJa8ZpoHjODg7O2PmzJl6y6hUKvj5+aF9+/Z6y0jpPDZ3nj9/DiLC+vXr9ZbJzMxEqVKlMGLECL1lnjx5Ai8vL9SoUUPQnUQ+SG5cAOCLL76AXC7n5bgbPnw4XF1dkZWVpbdMdHQ0mjdvLkRFi+Z9xx2fVWbbtm3h7+/Pa/dSq1YtDBo0SIiaDBNx//59EBG2bdumt4zmwp2+iUmFvoPFhSNHjvCOuJs+fTpsbGz0rvmSk5ODBg0aCAr0EYJRjIsm5NDZ2VnvKpP37t2DjY0Nr9XUV199BTc3N6FqWjRCVo2nTp3ivZrq2bOnwRX0GMZl9+7dICLcuHFDr/YqlQr+/v5o27at3mMI2T0XJ5YsWQK5XK63fzorKwuurq4YPny4Xu05jsPAgQMFX1EQglGMC/DujxEYGAhvb2+9I7qGDh2K0qVL4+XLl3q116ymhNyTKQ5ozrv5BFm0bt0aAQEBep/NTp8+HSVLlmSOWjNi3rx5sLOz03uHun79ehARTp06pVf7zZs3C/L7FSdGjhwJX19fvdvPnDkTNjY2egfPzJ8/H0SElStXCtSQP0YzLsC/aR6aNWumV5qHO3fuwNraWu9bw5o7GseOHTNUVYuFb6TOiRMneK04NVEofByMDNMyaNAg1KpVS6+2arUaAQEBaN26tV7tjeU8NneaN2+O6Ohovdq+fPkSZcqUwdChQ/Vqr0kLxfcejKEY1bgAwIEDB6BQKPTezg0ePBhly5bVy/n05s0byOVyJCUlGaqmRcP3jkHLli0RFBSk14/DtWvXQETYu3evoWoyjET9+vXRs2dPvdpqMpAfP35cZ1tD7loVN9zd3fVO3Dt79mxYW1vr5Tf5+++/UbJkSbRq1UpQQltDMLpxAYDFixeDiPRKNHnr1i0oFAq9o818fHwwevRoQ1W0ePjcjj569CiICBs3btTZVqlUwtbWFvPnzxdDTYbEcByHkiVL6hWZqVarERQUhBYtWuhsa0iWiOJGRkaG3pGZr169QtmyZREbG6uzbXp6Onx9fQ0qxWEIJjEuwLtoMIVCgQMHDuhsO3DgQJQrVw6vX7/W2bZDhw5o2bKlCBpaNmq1mldep8jISISEhOi1ewkJCcHgwYPFUJMhMQ8fPgQRYfPmzTrbbty4EUSk0yFsaH674saxY8dARDh//rzOtt988w0UCgVu3bpVaDulUokWLVqgVKlSuHbtmjiK8sRkxiU3NxfNmjWDq6sr/vnnn0Lb3rx5EwqFAnPnztXZ7/jx4+Hp6SmWmhYNn4y0hw8fBhFh06ZNOvv9+OOP0aBBA7HUZEjI3r17QUQ6f4DUajVCQkIQGRmps09NZm5jOo/NmaSkJMjlcrx586bQdq9fv0a5cuUwcOBAnX2OGjUKVlZW+OOPP8RSkzcmMy7Au4tDPj4+CAwM1Hkbv3///qhQoYLOCdBc2uRzu784c/PmTZQuXRpNmzbVGWTRtGlT1KxZU2cgQEJCAlxdXVnEmBnw/fffw9bWVmceOU2mB13plQytKVQcGTNmDHx8fHS2mzt3LhQKhc7koklJSSAi/PDDD2KpKAiTGhcA+Ouvv+Ds7Ix27doV6nC6ceMGrKysdJ7lnz17FkSEEydOiK2qxaJvFUBNSvCtW7cW2u7XX38FEfFOWsowPoMHD0ZISEihbTiOQ82aNXWWtDC0GmpxpWXLlujQoUOhbd68eYMKFSroLGlx+PBhWFtbIzY21uSLO5MbFwD4/fffIZfLdZbn7NOnD9zc3ArNSfT69WvIZDJBBa+KM5r65bqCLBo1aoTQ0NBCX9yrV6+CiLB//36x1WSITIMGDfDxxx8X2mbr1q0gIhw8eLDANqZ2Hpsznp6eGD9+fKFt5s+fDysrq0Ivut6+fRtly5ZFo0aNeKftl4IiYVyAd44qIsKaNWsKbHPt2jXI5XKd272qVavi888/F1tFiycuLg4KhaJQo7B//34QEbZv315gG6VSCWtrayxYsEAKNRkiwXEcXF1dkZCQUGib0NBQNGrUqMA27zuPr1+/LoGmlktmZqbO3723b9/Czc0Nffr0KbDNy5cvERISgipVquDp06cSaMqfImNcOI5D3759YWtrW+iRVu/eveHu7l7oDfN27dqhTZs2Uqhp0SiVSkRGRsLV1bXAFRLHcWjQoAFq165d6O4lKChI5zEbw7SkpaWBiPDrr78W2Gb79u06d6EjR46ElZUVu9skgJMnT4KICi3W9cMPP0AulxcYdKFWq9GxY0c4OTnh0qVLUqnKmyJjXIB3afPr1auHChUqFJjW4O+//4ZcLkdiYmKB/YwbNw5eXl4SaWnZaIIsAgICCgyK0EQYFXZHJiYmptDVLsP0aHahV65c0fqc4zjUrl0bDRo0KHAhoXEes12qMFasWAGZTFbgNYvs7Gy4u7sXWg5h4sSJkMlkvBKPGoMiZVwA4PHjx/D09ERYWFiBf/CePXvCw8OjwN3LqlWrQER65yRj5OfKlSuFBllwHIf69esjPDy8wB+dqVOnomzZslKryjCABQsWwNrausBIsd9++63QbAt//vknrK2tMXjwYJM7j82Vzz//HFWrVi3weWJiIuRyOa5evar1uaYCL58Ev8aiyBkX4F0lRAcHB3Tr1k3rS/vXX39BJpNh8eLFWuVPnz4NIsLp06elVtVi0QRZjBs3TutzTSbdXbt2aX2+YcMGEBGePHkipZoMAxg2bBiCgoK0PuM4DnXq1EG9evW0fgdv3bqFMmXKoHHjxnrlCWRop02bNmjXrp3WZ9nZ2fDw8ECPHj20Pj99+jTs7OzQs2fPImnci6RxAf69DVyQs7F79+6oVKmS1qiIly9fgoiQnJwstZoWzbfffltguWOO4xAREYG6detqfbFTU1N1RhgxTEujRo0QExOj9dmuXbsKrCr68uVLBAcHFynnsbni5eVV4AJu8eLFkMlkWsuUPHjwAG5ubggPDy+yFT2LrHEBgPj4+AIdjqmpqZDJZFi6dKlW2cImjaEfmiALGxsbrYkKd+7cCSLCnj17PniWk5MDhUKBhQsXGkNVhgDKli2L+Pj4Dz7nOA5169ZFRETEBwsHtVqNqKgoODk54fLly8ZS1SIpbBGck5ODSpUqoXv37h88e/PmDcLDw+Hm5laks48XaeOiVqvRtWtXODg44MKFCx88j4mJQeXKlbVuywvbbjL0RxNkUb58+Q+CLDiOQ3h4OOrXr6919xIQEIC4uDhjqcrgwZMnT0BE2LBhwwfP9uzZAyLCzp07P3j21VdfFUnnsTlS2PH90qVLIZPJPsj7x3EcevbsCTs7uyJ/7F+kjQvw7lJkrVq1UKlSJaSlpeV7dunSJRCR1hT7uhxlDP3RBFmEhoZ+EGRRmNO3S5cuOm91M0yDJtuCth+vgoI1fvzxRxARZs2aZUxVLZaCAo9yc3NRuXJlrUeWs2bNAhHhp59+MpaaginyxgUA7t69i/Lly6N+/fofRIh16dIFVapU+WD3oivEj8GP8+fPw8HBATExMfl+dDThqg0bNvxAZvLkyShfvrwx1WToycKFC6FQKD7wWe7bt09rmPmpU6dgZ2eHXr16FUnnsTlS0JWJ5cuXg4g+uLOybds2yGQyTJw40UgaGoZZGBcAOH78OGxsbNC/f/98L3dKSorWDKz6XE5i8EOTM2zatGn5Pt+2bRuI6IPyCT///DOISGfGZYbxiYuLQ0BAwAefN2zY8IMLshrncZ06dYqs89gc0XbZOzc3F1WrVkXnzp3zfX7p0iU4OTkhOjrabCp6mo1xAf7dRs6bNy/f59HR0fD29s4Xr5+VlaUzrQKDP1OnTv0gyEKTIqRx48b52mqOLXVl0mUYn6ZNm6JLly75Pjtw4ACIKJ8/5c2bN/joo4/g7u5epJ3H5oi2NFUrV64EESElJSXvs6dPn6JKlSoICQkxq7t7ZmVcAGDs2LGQy+X57lecP38eRIRVq1bla6tPQjgGPziOQ0xMDBwcHPIVN9qyZQuICIcOHcr7LDs7G1ZWVliyZIkJNGUURoUKFTB58uR8nzVu3DhfUlKO49CjRw/Y29vjzJkzplDTYtGWYFepVMLb2xvR0dF5n+Xk5KBRo0YoW7Ysbt++bQpVBWN2xkWlUqFt27ZwcXHJd2s1KioK1apVy7d70SeVNYM/r1+/RmhoaL4gi4LSsvv5+eHTTz81hZqMAnj+/PkHTmGNg3/Lli15n82cOdNsnMfmhrbSIJqTGc2ijeM4DB48GNbW1ma5+zc74wK8yyRavXp1VKtWDenp6QD+naz3j8H0LcLD4I+2IAttBaU6deqkV/VChvHQVBV932HctGlT1KhRI2/XsnXrVrNyHpsbmqKGWVlZAN7tWqpVq4aoqKi8NgsWLCgwGtYcMEvjAgDXr1+Hq6srIiMj83Yr7dq1g5+fX14+LH3LhzKEcfz4cdja2qJfv37gOA5qtRrBwcFo3rx5XpuJEyfCzc3NhFoy/suSJUtgZWWVtyjQGBuNH+3ixYtm5zw2N/5bjn3t2rUgorzjx71798LKygqjRo0ylYoGY7bGBXgXNmllZZV37KK5lPTjjz8CAI4dOwYi0noBkyEOq1evBhFh7ty5AP7NKXbs2DEA/96NyMjIMKGWjPcZOXIk/Pz88v6/efPmCA4OhlqtxpMnT1C5cmWzcx6bG1FRUWjZsiWAd0f9fn5+eZe+r127hlKlSqFly5Y6y08XZczauADvsoYSUV4amDZt2qB69epQqVR48eIFiAjr1q0zsZaWjSbI4vfff4darUZQUFDeF0cTKn706FETa8nQEBkZiU6dOgH4dwG2YcMG5OTkoGHDhmbpPDY3fHx8MGbMGAD/LsBOnz6NFy9ewN/fH76+vma/IDN74wIAQ4cOhUKhwKFDh/Lut2ickO7u7vjqq69MrKFlowmycHZ2xpUrV/Lut5w4cQJv376FXC7HsmXLTK0m4//j5uaW50tp2bIlgoKCoFKpEBsba7bOY3PizZs3kMvlSEpKgkqlQvXq1dGmTRuoVCq0atUKJUuWxN9//21qNQ3GIoxLbm4umjRpgjJlyuDmzZto1aoVAgMDoVar0bx583yhfQxpyMzMREBAAHx8fPD06VMEBASgdevWAIBq1aph9OjRJtaQAQAZGRl5R8cnTpwAEeHnn3/GDz/8ACLC8uXLTa2ixXPhwoW8o2NNPZYTJ07gs88+g1wu15qJ2hyxCOMCAM+ePUPVqlURFBSEP/74A0SEX3755YPzZYZ03LhxIy/IQhMNc/LkyXznywzT8r4fsnXr1qhevTp27doFKysrtgAwEppjsOfPnyMwMBAtW7bMuzw5f/58U6snGnKyEEqXLk3bt2+nO3fu0IIFCygyMpISEhKoevXqdOPGDcrJyTG1ihaPt7c3bdy4kQ4ePEgnTpwgf39/SkhIoMDAQEpNTTW1egwiSk1NJblcTi9fvqSdO3fSwIEDqXv37hQZGUmzZ882tXrFgtTUVHJ3d6f9+/dTamoqderUiQYPHkwDBw6kESNGmFo98TC1dRObHTt2QCaToXfv3iAihIaGgoigUCjg6uqK/v37s3xjErNw4UIQEfr378/moAhw9uxZ9O/fH66urpDL5ZDL5fD09ISnpyf8/Pzg5+dn9s7jos77cyCTyWBlZYVSpUqhZs2aKFeuHBo0aKC18KE5Y3HGBfg3LbW2/xQKBYgIsbGxZh3mV9QZMmQImwMTo1QqERsbm+9v/t//bGxsPki7zxAPfebAycnJIvO2Wcyx2Pv8888/BT5TqVRERLRs2TIaPny4sVQqdmj+zoU9Y3MgLcOHD6dly5YRUcHzkZubS/PnzzemWsUKfebg1atXFB8fb0StjIMMAEythJicO3eOwsLC9G5/9uxZCg0NlVCj4gebA9PD5sD0FPc5sLidS2JiIikUCr3aKhQKWrhwocQaFT/YHJgeNgemp7jPgcXtXEqXLk3p6el6t3d1daXnz59LqFHxg82B6WFzYHqK+xxYnHGxsbEhpVKpd3tra2vKzc2VUKPiB5sD08PmwPQU9zmwuGOxEiVKSNqeoRs2B6aHzYHpKe5zYHHGpWPHjrzOOaOjoyXWqPjB5sD0sDkwPcV9DizuWKy4R2gUBdgcmB42B6anuM+Bxe1cQkNDKTY2lmQyWaHtZDIZxcbGWtRkFhXYHJgeNgemp9jPgenub0pHYbdi2e1w48DmwPSwOTA9xXkOLNK4aDh79iwGDBgAV1dXWFtbw9XVFQMGDGB5rYwImwPTw+bA9BTHObA4nwuDwWAwTI/F+VwYDAaDYXqYcWEwGAyG6DDjwmAwGAzRYcaFwWAwGKLDjAuDwWAwRIcZFwaDwWCIDjMuDAaDwRAdZlwYDAaDITrMuDAYDAZDdJhxYTAYDIboMOPCYDAYDNFhxoXBYDAYosOMC4PBYDBEhxkXBoPBYIgOMy4MBoPBEB1mXBgMBoMhOsy4MBgMBkN0/h+Lziri7R5dtgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 500x800 with 70 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a tree case\n",
    "model = KAN(width=[4,6,2,6,1], mult_arity=4, grid=5, k=3) # note [0,1] means in the output layer, 0 sum node and 1 mult node\n",
    "x = torch.rand(100,4)*2-1\n",
    "\n",
    "model.module(0,'[0,1]->[0,1,2]->[0,1,2]->[0]')\n",
    "model.module(0,'[2,3]->[3,4,5]->[3,4,5]->[1]')\n",
    "model.module(2,'[0]->[0,1,2]')\n",
    "model.module(2,'[1]->[3,4,5]')\n",
    "\n",
    "model(x)\n",
    "model.plot(beta=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05cf43c8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
